>Логарифмічні рівняння>Що таке логарифмічні рівняння?

Що таке логарифмічні рівняння?

Логарифмiчнi рiвняння — це рiвняння, що мiстять змiнну $x$ в основi логарифма. Щоб винести $x$ , повнiстю позбувшись логарифма, потрiбно застосовувати логарифмiчнi властивостi або показники степенiв. Коли використовується десятковий логарифм $\log$ , в основi маємо число $10$ , а коли використовується натуральний логарифм $\ln$ , в основi маємо число $e$ .

Теорiя

Логарифмiчнi рiвняння

У логарифмiчних рiвняннях для того, щоб позбутися логарифма, потрiбно винести показник перед основою

10

або

e

по обидва боки рiвняння. Використовуємо основу

10

, коли маємо справу з десятковим логарифмом, i

e

, коли маємо справу з натуральним логарифмом.

\begin{array}{l} \log x & = c & \ln x & = c \\ 1 0^{\log x} & = 1 0^{c} & e^{\ln x} & = e^{c} \\ x & = 1 0^{c} & x & = e^{c} \end{array}

Зверни увагу! Логарифмувати можна лише додатнi числа.

Приклад 1

Розв’яжи логарифмiчне рiвняння $\ln x = 4$

\begin{array}{l} ln x = 4 e^{\ln x} & = e^{4} x & = e^{4} x & \approx 54.6Приклад 2 Розв’яжи логарифмiчне рiвняння \frac{1}{4} \log 2 x = 8 \begin{array}{l} 14 \ln 2 x = 8 | \cdot 4 \ln 2 x & = 32 e^{\ln 2 x} & = e^{32} 2 x & = e^{32} & | : 2 x & = \frac{e^{32}}{2} \approx 3.95 \cdot 1 0^{13}Приклад 3 Розв’яжи логарифмiчне рiвняння 5 \ln (x + 2) = 15 \begin{array}{l} 5 \lnПопередня стаття Що таке показникові рівняння? Наступна стаття Як розв'язувати показникові нерівностіПовернутисяДодому Навчальний план Статистика ЛігаПро нас Про House of Math Співробітники Працевлаштування в House of Math Медіа Лекції Блог Контактна інформація support@houseofmath.com Адреса House of Math 470 Ramona Street Palo Alto, CA 94301 USA FAQ Корисні посилання WeTakeAction Магія математики для України Репетиторство Джуніор-матем Вправи з ручкою та папером Енциклопедія Мова/Навчальна програма Умови Політика конфіденційності Політика щодо файлів cookies Завантажте наш додаток{"props":{"pageProps":{"campaign":false,"articleBody":" Логарифмiчнi рiвняння — це рiвняння, що мiстять змiнну x в основi логарифма. Щоб винести x, повнiстю позбувшись логарифма, потрiбно застосовувати логарифмiчнi властивостi або показники степенiв. Коли використовується десятковий логарифм log ⁡ , в основi маємо число 10, а коли використовується натуральний логарифм ln ⁡ , в основi маємо число e. Теорiя Логарифмiчнi рiвняння У логарифмiчних рiвняннях для того, щоб позбутися логарифма, потрiбно винести показник перед основою 10 або e по обидва боки рiвняння. Використовуємо основу 10, коли маємо справу з десятковим логарифмом, i e, коли маємо справу з натуральним логарифмом. log ⁡ x = c ln ⁡ x = c 10log ⁡ x = 10c eln ⁡ x = ec x = 10c x = ec Зверни увагу! Логарифмувати можна лише додатнi числа. Приклад 1 Розв’яжи логарифмiчне рiвняння ln ⁡ x = 4 ln ⁡ x = 4 eln ⁡ x = e4 x = e4 x ≈54.6 Приклад 2 Розв’яжи логарифмiчне рiвняння 1 4 log ⁡ 2x = 8 1 4 ln ⁡ 2x = 8 | ⋅ 4 ln ⁡ 2x = 32 eln ⁡ 2x = e32 2x = e32 |:2 x = e32 2 ≈3.95 ⋅ 1013 Приклад 3 Розв’яжи логарифмiчне рiвняння 5 ln ⁡ (x + 2) = 15 5 ln ⁡ (x + 2) = 15|:5 ln ⁡ (x + 2) = 3 eln ⁡ (x+2) = e3 x + 2 = e3 x = e3 − 2 e3 − 2 ≈ 20.1 − 2 x ≈ 18.1 ","topic":{"breadcrumbs":[{"_key":"c0cf1a4b-5f7d-5390-9a52-e6ae2428b50c","h1":"Енциклопедія","path":"/encyclopedia"},{"_key":"58d8130f-e1b9-56b5-a4aa-04a4be9d7874","h1":"Алгебра","path":"/encyclopedia/alhebra"},{"_key":"c06d9fed-d452-510c-9284-c1dc6294a8c5","h1":"Логарифми","path":"/encyclopedia/alhebra/loharyfmy"},{"_key":"f05334ae-9371-5feb-aa08-b192c5696de2","h1":"Логарифмічні рівняння","path":"/encyclopedia/alhebra/loharyfmy/loharyfmichni-rivnyannya"},{"_key":"01431cfe-84f9-558a-9224-1a26e49616f1","h1":"Що таке логарифмічні рівняння?","path":"/encyclopedia/alhebra/loharyfmy/loharyfmichni-rivnyannya/shcho-take-loharyfmichni-rivnyannya"}],"cssUrl":"/29f93770-5a57-4692-a0bc-b7641ad6003c-uk-5.css","h1":"Що таке логарифмічні рівняння?","htmlContent":{"html":" \u003c/p\u003e\u003cp class=\"indent\" \u003e     Логарифмiчнi рiвняння — це рiвняння, що мiстять змiнну \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/math\u003e в основi логарифма. Щоб винести \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/math\u003e, повнiстю позбувшись логарифма, потрiбно застосовувати логарифмiчнi властивостi або показники степенiв. Коли використовується десятковий логарифм \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi class=\"qopname\"\u003e log\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e\u003c/math\u003e, в основi маємо число \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/math\u003e, а коли використовується натуральний логарифм \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi class=\"qopname\"\u003e ln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e\u003c/math\u003e, в основi маємо число \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/math type=\"punct\"\u003e. \u003c/p\u003e                                                                                                                                                                                                                                               \u003cdiv class=\"tcolorbox fooinfo\" id=\"tcolobox-616\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Теорiя\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"info-container-title\"\u003e \u003cspan  class=\"larm-2074\"\u003eЛогарифмiчнi\u003c/span\u003e \u003cspan  class=\"larm-2074\"\u003eрiвняння\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003eУ логарифмiчних рiвняннях для того, щоб позбутися логарифма, потрiбно винести показник перед основою \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/math\u003e або \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/math\u003e по обидва боки рiвняння. Використовуємо основу \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/math\u003e, коли маємо справу з десятковим логарифмом, i \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/math\u003e, коли маємо справу з натуральним логарифмом. \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                           \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi class=\"qopname\"\u003e log\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                      \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmi  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class=\"align-odd\"\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmi class=\"qopname\"\u003elog\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003c/mtd\u003e                               \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmi  \u003ec\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                               \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmi class=\"qopname\"\u003eln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmi  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\u003ex\u003c/mi\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmi  \u003ec\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                               \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                        \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmi  \u003ec\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                               \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                               \u003cmtd  class=\"align-label\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                               \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                               \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e   \u003c/div\u003e  \u003c/div\u003e                                                                                                                                                                                                                           \u003cp class=\"indent\" \u003e     \u003cb\u003eЗверни увагу!\u003c/b\u003e Логарифмувати можна лише додатнi числа. \u003c/p\u003e \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-617\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Приклад 1\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003eРозв’яжи логарифмiчне рiвняння \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi class=\"qopname\"\u003eln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                      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class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                        \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                                      \u003cmtd  class=\"align-label\"\u003e                                                       \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e≈\u003c/mo\u003e\u003cmstyle  class=\"text\"\u003e\u003cmtext  \u003e\u003c/mtext\u003e\u003cmstyle  class=\"math\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmo  class=\"MathClass-punc\" type=\"punct\"\u003e.\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003c/mstyle\u003e\u003cmtext  \u003e\u003c/mtext\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                              \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e   \u003c/div\u003e  \u003c/div\u003e \u003cp class=\"noindent\" \u003e\u003c/b\u003e                                                                                                                                                                                                                                          \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-618\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Приклад 2\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003eРозв’яжи логарифмiчне рiвняння \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmfrac\u003e\u003cmrow\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e \u003cmrow\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfrac\u003e\u003cmi class=\"qopname\"\u003e log\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e8\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"alignat-star\"\u003e                           \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmfrac\u003e\u003cmrow  \u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e \u003cmrow  \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfrac\u003e\u003cmi class=\"qopname\"\u003e ln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                     \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e8\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-even\"\u003e\u003c/mrow\u003e\u003cmo class=\"MathClass-close\" fence=\"true\" mathsize=\"1.61em\" \u003e|\u003c/mo\u003e\u003c/mrow\u003e \u003cmo  class=\"MathClass-bin\"\u003e⋅\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                          \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-label\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                          \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-label\"\u003e                           \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi class=\"qopname\"\u003e ln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                       \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                           \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-even\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                               \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-label\"\u003e                           \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmi class=\"qopname\"\u003eln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                            \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-even\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                             \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-label\"\u003e                                      \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                            \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-even\"\u003e\u003c/mrow\u003e\u003cmo class=\"MathClass-close\" fence=\"true\" mathsize=\"1.19em\" \u003e|\u003c/mo\u003e\u003c/mrow\u003e\u003cmo  class=\"MathClass-punc\" type=\"divide\"\u003e:\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                           \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-label\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                          \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                          \u003cmtd  class=\"align-label\"\u003e                           \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                           \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmfrac\u003e\u003cmrow  \u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003c/mrow\u003e    \u003cmrow  \u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfrac\u003e  \u003cmo  class=\"MathClass-rel\"\u003e≈\u003c/mo\u003e\u003cmstyle  class=\"text\"\u003e\u003cmtext  \u003e\u003c/mtext\u003e\u003cmstyle  class=\"math\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmo  class=\"MathClass-punc\" type=\"punct\"\u003e.\u003c/mo\u003e\u003cmn\u003e9\u003c/mn\u003e\u003cmn\u003e5\u003c/mn\u003e\u003c/mstyle\u003e\u003cmtext  \u003e\u003c/mtext\u003e\u003c/mstyle\u003e \u003cmo  class=\"MathClass-bin\"\u003e⋅\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                     \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-even\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                             \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e   \u003c/div\u003e  \u003c/div\u003e \u003cp class=\"noindent\" \u003e\u003c/b\u003e                                                                                                                                                                                                                    \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-619\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Приклад 3\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003eРозв’яжи логарифмiчне рiвняння \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmi class=\"qopname\"\u003e ln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmspace width=\"-0.17em\" class=\"negthinspace\"/\u003e \u003cmrow\u003e\u003cmo fence=\"true\" form=\"prefix\"\u003e(\u003c/mo\u003e\u003cmrow\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003cmo fence=\"true\" form=\"postfix\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e5\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                              \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmi class=\"qopname\"\u003e ln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmspace width=\"-0.17em\" class=\"negthinspace\"/\u003e \u003cmrow\u003e\u003cmo fence=\"true\" form=\"prefix\"\u003e(\u003c/mo\u003e\u003cmrow\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003cmo fence=\"true\" form=\"postfix\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/mtd\u003e                             \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmspace width=\"1em\" class=\"quad\"/\u003e\u003c/mrow\u003e\u003cmo class=\"MathClass-close\" fence=\"true\" mathsize=\"1.19em\" \u003e|\u003c/mo\u003e\u003c/mrow\u003e\u003cmo  class=\"MathClass-punc\" type=\"divide\"\u003e:\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                 \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                             \u003cmtd  class=\"align-label\"\u003e                              \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi class=\"qopname\"\u003e ln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmspace width=\"-0.17em\" class=\"negthinspace\"/\u003e \u003cmrow\u003e\u003cmo fence=\"true\" form=\"prefix\"\u003e(\u003c/mo\u003e\u003cmrow\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003cmo fence=\"true\" form=\"postfix\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/mtd\u003e                               \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                             \u003cmtd  class=\"align-label\"\u003e                              \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmi class=\"qopname\"\u003eln\u003c/mi\u003e\u003cmo\u003e ⁡ \u003c/mo\u003e \u003cmspace width=\"-0.17em\" class=\"negthinspace\"/\u003e\u003cmrow\u003e\u003cmo fence=\"true\" form=\"prefix\"\u003e(\u003c/mo\u003e\u003cmrow\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/mrow\u003e\u003cmo fence=\"true\" form=\"postfix\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003c/mtd\u003e                                                 \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-label\"\u003e                                           \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmsup\u003e\u003cmrow  \u003e\u003cmi  \u003ee\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow  \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup  \u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e         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Вивчай математику швидко та легко. 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безплатно","continueForFree":"Продовжити безплатно","joinNow":"Приєднайся зараз","startNow":"Почати зараз","changePlan":"Змінити план","currentPlan":"Поточний план","upgrade":"Оновити","bestValue":"Найкраща ціна","knowitSpecialOffer":"KNOWIT SPESIALTILBUD","getAccessTo":"Отримай доступ до","signUp":"Зареєструватися","cancelAnytime":"Скасуй у будь-який час","couponPeriodPlural":"протягом {{durationInMonths}} місяців","couponPeriodSingular":"протягом 1 місяця","couponOnce":"протягом a {{ interval }} період","afterTime":"Потім","freeTrialPeriodPluralCheckout":"{{ freeTrialPeriod }}-денна Безплатна пробна версія","freeTrialPeriodSingular":"1-денну Безплатна пробна версія","freeTrialPeriodPlural":"{{ freeTrialPeriod }}-денна Безплатна пробна версія","seeMore":"Побачити більше","close":"Закрити","showAllPackages":"Показати менше пакетів","showLessPackages":"Показати всі пакети","textYearly":"{{ price }} стягується щорічно","testFreeTrialPeriod":"Спробуй {{trialDays}}-денну безплатну пробну версію ","startFreeTrialPeriod":"🚀 Розпочати {{ trialDays }} денну безплатну пробну версію","unlockTrialPeriod":"Розблокуй {{ trialDays }}-денну безплатну пробну версію ","then":"потім","buy":"Buy","whatsIncluded":"See what's included","showLess":"Show less","savePercentage":"Save {{savedPercentage}}%"},"product":{"title":"Отримай свій власний індивідуальний шлях навчання","faq":"Часті запитання","faqLogo":"Логотип Частих запитань","teacher":"Я — вчитель/-ка","products":{"videoCourses":{"title":"Твій шлях до опанування математики","tagline":"Bootcamps","text":"Цифрові курси з навчальними відео та інтерактивним розв’язанням завдань"},"keepTrack":{"title":"Відстежуй прогрес","tagline":"Панель статистики","text":"Твоя власна панель статистики для відстеження прогресу"},"unlimitedQuestions":{"title":"Необмежена кількість запитань","tagline":"Цілодобовий математичний чат","text":"Постав необмежену кількість запитань нашим репетиторам у нашому математичному чаті."},"excercises":{"title":"Усе, що тобі потрібно, в одному місці","tagline":"Завдання","text":"Отримай доступ до повного навчального плану K-12"}}},"checkout":{"title":"Subscription checkout","metaDescription":"Checkout"},"success":{"title":"Success","metaDescription":"Success","date":"Дата замовлення","confirmationNumber":"Номер підтвердження","welcome":"Ласкаво просимо в","fullAccess":"Тобі надано доступ до House of Math!","goHomeButton":"На головну","backToUrl":"Повернутися до того місця, де ти зупинився/зупинилася","yourSubscriptionPackage":"Пробний період закінчується","trialPeriodEndsOn":"Твій пакет підписки","packageUpgraded":"Пакет оновлено","packageChanged":"Пакет змінено","checkmark":"Логотип галочки","getStarted":"Розпочати"},"callback":{"text":"Ви майже досягли мети – ми обробляємо ваш тарифний план"},"paymentFailed":{"message":"Ми не можемо обробити твій платіж.\nБудь ласка, спробуй ще раз.","tryAgain":"Повернутися","cancelled":"Не вдалося здійснити платіж","refused":"Не вдалося здійснити платіж","error":"Не вдалося здійснити платіж","metaDescription":"Не вдалося здійснити платіж","refusedSubtitle":"Будь ласка, спробуйте ще раз, використовуючи інший спосіб оплати або картку.","errorSubtitle":"Під час обробки вашого платежу сталася помилка.\nБудь-ласка спробуйте пізніше."},"paymentPending":{"title":"Обробка платежу","metaDescription":"Обробка платежу","message":"Твій платіж обробляється","messageEmailSent":"Електронний лист з підтвердженням буде надіслано на електронну пошту \u003cemail\u003e{{email}}\u003c/email\u003e"},"modal":{"title":"Зареєструватися на безплатну пробну версію","text":"Дякуємо, що ти знову з нами!","button":"Get unlimited access","freeVersion":"Continue to use free version","dashboard":{"register":"Зареєструватися","registerFree":"Зареєструватися безкоштовно","fullAccess":"Отримай повний доступ","startFree":"Почати безкоштовно"}},"onboarding":{"learningPath":"Створення твого шляху навчання","choosePlan":"Обери план, що відповідає твоїм потребам"}},"chat":{"expressionError":"Щось пішло не так із цим виразом","header":"Чат із репетитором","infoBox":"Вітаю! \u003cbr\u003e\u003cbr\u003e Будь ласка, постав свої запитання з математики тут. Можливо, ми не зможемо відповісти на запитання з математики університетського рівня.","infoBoxEnd":"Цей чат безплатний тільки протягом обмеженого часу. У чаті ми спілкуємося тільки англійською мовою.","infoBoxItem1":"1. Сформулюй конкретну проблему.","infoBoxItem2":"2. Зазнач усі подробиці.","infoBoxItem3":"3. Опиши, що ти вже спробував/спробувала зробити.","infoBoxList":"Поради щодо якнайшвидшого отримання допомоги:","infoMessage":"Постав запитання репетитору. Ми відповімо, щойно зможемо.","tutorChat":{"alreadyClaimed":"Хтось прийняв цей чат до тебе.","chatHeader":"Ідентифікатор користувача {{userId}}","claimThread":"Прийняти чат","claimWarning":"Прийнявши чат, ти маєш відповісти на нього та надати повну відповідь.","end":"Завершити чат","endWarning":"Завершивши чат, ти більше не зможеш відповісти цій людині.","listActiveChat":"Мої активні чати","listHeader":"Повідомлення","listQueue":"Черга","noActiveChat":"Ти не маєш активних чатів","noNewMessages":"Нових повідомлень немає","offline":"В мережі","online":"Не в мережі","onlineStatus":"Онлайн-статус"},"newMessage":"Постав своє запитання тут","noTeachersAvailable":"Зараз немає вільних репетиторів","onlineTeachers":"Репетитори онлайн","openingHours":"Працюємо 24/7 \u003cbr\u003e Чат англійською мовою","receivedMessage":"Ми отримали твоє повідомлення та відповімо якнайшвидше!"},"chatAi":{"consentText":"Привіт! Я — Оракул, твій математичний штучний інтелект (AI). Я готовий допомогти тобі з навчанням","ctaAsk":"Запитати Оракула","ctaLearningPath":"Мій шлях навчання","askHelp":"Чим я можу допомогти?","networkError":"Вибач, трапилася помилка. Спробуй пізніше.","unauthorizedError":"Ой-ой!","rateError":"Ой-ой! Здається, було використано всю твою денну квоту як безплатного користувача. Щоб продовжити, онови підписку.","rateErrorSubscribed":"Ой-ой! Здається, Оракул зараз дуже завантажений. Спробуй пізніше. ","exitOracle":"Значок","placeholder":"Запитай мене щось...","subscribe":"Зареєструватися","betaString":"Бета","globeAlt":"AI Глоуб","oracleImageAlt":"Образ Oracle","unauthorizedMessage":"Почни використовувати безплатну пробну версію і я відповім на твоє питання","user":"Користувач","backToActivity":"Назад до активності","send":"Відіслати","welcomeMessage":"Пам'ятай, я завжди тут, щоб допомогти тобі!","alwaysHereForYou":"Я завжди тут для тебе","autoTriggeredHelp":"Схоже, це трохи складно — можу допомогти?","solvedCelebration":"Так тримати – це правильна відповідь! 🎉 Продовжимо?"},"userFeedback":{"imageAlt":{"veryDissatisfied":"Дуже незадоволений(-а)","dissatisfied":"Незадоволений(-а)","neutral":"Нейтрально","satisfied":"Задоволений(-а)","verySatisfied":"Дуже задоволений(-а)","placeHolder":"Оціни","close":"close","feedbackButton":"Залишити відгук"},"header":"Маєш якийсь відгук?","commentBox":"Напиши свій коментар тут (необов'язково)","feedbackButtonText":"Відгук","sendButtonText":"Надіслати","errorMessage":"Трапилася помилка.","alreadySubmittedToday":"Ти вже залишив(-ла) відгук про це сьогодні","thanksForFeedback":"Дякуємо за твій відгук!","appreciationMessage":"Ми цінуємо, що ти знайшов(-ла) час поділитися з нами своїми думками."},"gemShop":{"buyNow":"Купити зараз","comingSoon":"Незабаром","itemTypes":{"chest":"Груди","head":"Голова","neck":"Шия","hats":"Мої Капелюхи","jewelry":"Мої Прикраси","clothes":"Мій Одяг","special":"Особливе"},"menu":{"pet":"пет","featured":"Обране"},"noGems":"Потрібно більше коштовностей","owned":"Куплено","store":"Крамниця","tier":"Статус","upgrade":"Оновити","upgradeTypes":{"productionRelativeIncrease":"Посилення коштовностей +{{value}}%","productionAbsoluteIncrease":"Посилення коштовностей +{{value}}","tickRateIncrease":"Швидкість таймера {{value}}x","energyCapacityIncrease":"Лайкоздатність +{{value}}"},"unlockRank":"Ранг дракона {{rank}}","Padlock":"Навісний замок","rankUp":"Щоб розблокувати цей елемент, підвищ рейтинг свого дракона","allItems":"Усі"},"homebase":{"mainView":"Головна","dragonView":"База","storeView":"Магазин","cavern":"Темна печера","checkBaseForQuests":"Перевір свій шлях навчання","chestText":"Це твоя база. Повертайся сюди, щоб переглянути тести та оновлення своєї математичної подорожі. Там ти знайдеш такі речі:","chestTitle":"Ласкаво просимо!","close":"Закрити","collection":"Моя колекція","collectionList":{"allItems":"Усі кубки","allRewards":"Усі нагороди","bootcamps":"Bootcamps","competition":"Змагання","mathdrill":"Основи математики","mathEssentials":"Основи математики"},"collectionShowcase":{"bootcamp":"Bootcamp","gathered":"Зібрано","championship-2021":"Чемпіонат з множення 2021"},"rankPopupTitle":"Нова система підвищення рівня XP!","rankPopupText":"Ти можеш здобути XP, виконуючи завдання на порталі. Досягнувши порогу XP, ти підвищиш рівень.","completed":"Завершено","weExchange":"Обмінюємо","dummyData":{"mult":{"title":"Множення","description":"Що таке множення?"},"algebra":{"title":"Алгебра","description":"Елементарна алгебра"}},"event":{"checkQuest":"Прочитано та зрозуміло","INTRO":{"dialogue":[{"text":"Це твоя база. Тут ти отримуватимеш повідомлення та завдання, збираючи скарби та нагороди під час своєї подорожі світом математики.","title":"Ласкаво просимо додому"}]}},"findYourLearningPath":"Знайди свій шлях навчання, створи аватар та отримай домашнього дракона!","gemBlueAlt":"Блискучий синьо-білий діамант","gemGreenAlt":"Блискучий зелений смарагд","gemRedAlt":"Сяйнистий червоний рубін","gotoavatarpage":"Перейти до аватара","Home":"Домашня база","homebasepage":"Початкова база:","imageAlt":{"goldenHex":"Золотий шестикутник","levelBadge":"Значок переходу на вищий рівень"},"introText":"Ти саме той герой/героїня, якого ми шукаємо. Ми повернемося до цього. Дозволь спочатку показати тобі все навколо.","introTitle":"Гарний початок!","kudos":"Kudos","level":"РІВЕНЬ","levelUp":"Підвищення рівня","navbarIcon":"Схованка","next":"Далі","shadow":"Тінь","playerName":"Ім'я гравця...","questCompleted":" Тест виконано!","questDescriptions":{"bootcamp":" Досліди bootcamp \u003cb\u003e{{BootcampTitle}}\u003c/b\u003e і здобудь перемогу над босом буткемпів!","essential":"Щоб підтвердити свої навички, пройди Основи математики!","encyclopedia":"Прочитай і зрозумій \u003cb\u003e{{EncyclopediaArticle}}\u003c/b\u003e  та постав відповідну позначку!"},"quests":"Мій математичний тест","mathQuests":"Математичні тести","completedMathQuests":"Виконані завдання","completeQuestsToSee":"Щоб побачити тести тут, потрібно їх виконати","questText":"Пройди діагностичний тест й отримай індивідальний шлях навчання","quiz":{"advancedQuizText":"Щоб рухатися вперед, тепер тобі потрібно лише обрати теми, які тобі знайомі.","advancedQuizTitle":"Чудові результати тесту!","advancedSubjects":{"quiz-subject-advanced-derivatives":{"title":"Похідна"},"quiz-subject-advanced-differential-equations":{"title":"Диференціальні рівняння"},"quiz-subject-advanced-integrals":{"title":"Інтеграли"},"quiz-subject-advanced-logarithms":{"title":"Логарифми"},"quiz-subject-advanced-pi":{"title":"Число «Пі», π"},"quiz-subject-advanced-probability":{"title":"Теорій ймовірностей"},"quiz-subject-advanced-proofs":{"title":"Доведення"},"quiz-subject-advanced-quadratic-equations":{"title":"Квадратні рівняння"},"quiz-subject-advanced-series":{"title":"Числові ряди"},"quiz-subject-advanced-sets-of-numbers":{"title":"Числові множини"},"quiz-subject-advanced-trigonometry":{"title":"Тригонометрія"},"quiz-subject-advanced-vectors":{"title":"Вектори"}},"applyText":"Ти, очевидно, добре знаєш математику! Якщо ти бажаєш доєднатися до команди House of Math, будь ласка, подай заявку за посиланням \u003clinkToCareers\u003ehere\u003c/linkToCareers\u003e.","awardTitle":"Ми перетворюємо твій досвід навчання на гру","awardTitleSubtext":"Під час мандрівки ти знайдеш такі скрині з нагородами.","awesome":"Чудово!","buttonTakeQuiz":"Пройти тест","creatingYourLearningPath":"Створення твого шляху навчання...","learningPath":"Створення твого шляху навчання","greatResultsText":"Щоб рухатися вперед, тепер тобі потрібно лише обрати теми, які тобі знайомі.","greatResultsTitle":"Чудові результати тесту!","subjectKnowledgeRating":{"0":"Жахливо","1":"Погано","2":"Нейтрально","3":"Добре","4":"Чудово"},"subjects":{"quiz-subject-algebraic-factorization":{"questionRating":"Наскільки добре ти опанував/опанувала розкладання многочлена на множники?","title":"Розкладання многочлена на множники"},"quiz-subject-basic-algebra":{"questionRating":"Наскільки добре ти опанував/опанувала операції з математичними знаками?","title":"Основи алгебри"},"quiz-subject-equations":{"questionRating":"Наскільки добре ти опанував/опанувала рівняння?","title":"Рівняння"},"quiz-subject-fractions":{"questionRating":"Наскільки добре ти опанував/опанувала дроби?","title":"Дроби"},"quiz-subject-functions":{"questionRating":"Наскільки добре ти опанував/опанувала функції?","title":"Функції"},"quiz-subject-parentheses":{"questionRating":"Наскільки добре ти опанував/опанувала круглі дужки?","title":"Круглі дужки"},"quiz-subject-percent":{"questionRating":"Наскільки добре ти опанував/опанувала відсоток?","title":"Відсоток"},"quiz-subject-powers":{"questionRating":"Наскільки добре ти опанував/опанувала степінь числа?","title":"Степінь числа"},"quiz-subject-the-multiplication-table":{"questionRating":"Наскільки добре ти опанував/опанувала таблицю множення?","title":"Таблиця множення"}},"title":"Щоб навчання було ефективним, пройди тест!","titleSubtext":"Пройди цей тест, щоб дізнатися, з чого почати.","yesNoQuestionTitle":"Чи працював/працювала ти коли-небудь над \u003clowercase\u003e{{ subject }}\u003c/lowercase\u003e?"},"retakeQuiz":"Повторити тест","reward":"Нагорода","storyCards":{"buttonCool":"Класно!","buttonIWill":"Я буду!","buttonJump":"Стрибай","buttonLetUsTry":"Спробуймо!","buttonNice":"Чудово!","buttonOfCourse":"Звісно!","buttonOh":"О!","buttonPeekaBoo":"Піка Бу","buttonRoar":"Рев","buttonThanks":"Дякую!","buttonWow":"Овва!","buttonYes":"Так!","ChoosePetTrick":"Твій дракон готовий навчитися нового трюку! Обери один із трьох нижче!","ChooseYourEgg":"Дивися, хтось залишив тобі подарунок!","CoolDown":"Тобі потрібно зачекати певний час, перш ніж ти знову зможеш віддати математичну енергію! Використай цей час, щоб зібрати більше енергетичних сфер в  Основах математики","CoolDownFirstTime":"Твоє яйце повне, й потрібно трохи зачекати, перш ніж можна буде віддати більше математичної енергії! Використай цей час, щоб зібрати більше математичної енергії зі скринь в Основах математики!»","DoNotHaveEnoughMnO":"Ти більше не маєш енергії лайків! Щоб здобути більше, виконай тести!","DragonFull":"Твій дракон ситий! Зачекай певний час, перш ніж давати йому енергію лайків.","DragonTrickCooldown":"Твій дракон утомився після навчання нового трюку. Перш ніж пробувати знову, дозволь йому трохи відпочити!","DragonTrickNotWilling":"Твій дракон не бажає тренуватися, доки не буде щасливий і нагодований!","DragonTutorial1":"Дбай про здоров’я свого дракона, годуючи його енергією лайків!","DragonTutorial2":"Ходять чутки, що якщо ти деякий час підтримаєш свого Дракона здоровим, він може навчитися нових трюків!","DragonTutorial3":"Дракони також потребують пестощів! Регулярно гладь свого дракона!!","DragonTutorial4":"Молодець! Твій Дракон щасливий! Продовжуй дарувати йому любов щодня!","EggHasBeenChosen":"Чудовий вибір! Пропоную безпечно помістимо яйце у твою базу. Чи зможемо ми змусити його вилупитися?","EggHungry1":"Гм... . Твоє яйце здається голодним!","EggHungry2":"Ось, візьми цю енергію лайків!","EggHungry3":"Спробуй нагодувати яйце енергією лайків, натиснувши на нього!","EggInfoStillHatching":"Твоє яйце зараз вилуплюється! Проте потрібно згодувати йому ще енергії лайків!","EggIsAboutToHatch":"Неймовірно! Тепер ти маєш Дракона на своїй домашній базі","FeedMathEnergyToEggFirstTime":"Спробуй нагодувати яйце енергією лайків, натиснувши на нього!","FirstTimeGettingMathEnergyFromChest":"Круто! Ти знайшов свою першу енергетичну сферу! Віддай її своєму яйцю на домашній базі!!","GiveDragonName":"Введи ім'я дракона або просто натисни OK.","InfoAboutPetTrick":"Твій дракон може вчитися, коли він ситий і задоволений!","MathEnergyTutorial1":"Щоб яйце вилупилося, потрібно нагодувати його достатньою кількістю енергії лайків.","MathEnergyTutorial2":"Щоб здобути більше енергії лайків, виконай тести!","NextHatchingState1":"Овва! Глянь! Твоє яйце тепер має інший вигляд!","NextHatchingState2":"Твоє яйце тріснуло ще трохи! Цікаво, що всередині...","NextHatchingState3":"Ще трохи... Твоє яйце скоро вилупиться!","TimesTableCompetition2021FirstPlace":"Вітаємо з перемогою в Чемпіонаті з множення 2021 року! Отримай унікальний кубок і додай його до своєї колекції.","TimesTableCompetition2021Participant":"Дивовижна робота! Ти заробив/заробила цей приз, беручи участь у Чемпіонаті з множення 2021 року.","TimesTableCompetition2021SecondPlace":"Вітаємо з 2-м місцем у Чемпіонаті з множення 2021 року! Отримай унікальний кубок і додай його до своєї колекції.","TimesTableCompetition2021ThirdPlace":"Вітаємо з 3-м місцем у Чемпіонаті з множення 2021 року! Отримай унікальний кубок і додай його до своєї колекції."},"space":"Пробіл","takeTheQuiz":"Пройди тест, щоб розблокувати свій дім!","tooltip":{"videoCourse":"Bootcamp","encylopedia":"Енциклопедія","mathEssential":"математичні вишколи","description":{"videoCourse":"Дивися відео, виконуй завдання та здобудь перемогу над босом буткемпів","encylopedia":"Прочитай і зрозумій та постав відповідну позначку!","mathEssential":"Щоб підтвердити свої навички, пройди Основи математики!"}},"titles":{"houseOfMathMember":"Член House of Math","mathApprentice":"Математик-практикант","mathemagician":"Матемаг","mathJunior":"Математик-початківець","mathlete":"Мататлет","mathScholar":"Математик-експерт","mathSorcerer":"Математик-чудотворець"},"unlockYourHomebase":"Увійди або зареєструйся, щоб перейти до особистого кабінету, де можна створити свій індивідуальний шлях навчання, відстежувати здобуті бали досвіду (XP) та винагороди, отримати доступ до своєї Схованки й багато іншого!","updateQuests":"Оновити навчальні тести","xp":"XP","open":"ВІДЧИНЕНО","yourCompletedQuests":"Твої виконані квести","yourFirstQuest":"Твій перший квест","yourNextQuest":"Твій наступний квест","yourUpcomingQuests":"Твої майбутні квести","removeTask":"Видалити зі шляху навчання","cancel":"Скасувати","rank":"Ранг","leagueNavButton":"Ліга","menuLabel":"Меню","loading":"Завантаження","loadscreenHint":{"feedDragon":"Підвищ рейтинг свого дракона, годуючи його енергією лайків","earnKudos":"Заробляй енергію лайків, виконуючи математичні завдання","earnGems":"Заробляй коштовності, виконуючи математичні завдання","buyStuff":"Купуй круті речі з коштовностями в крамниці дракона","wardrobe":"Усі куплені речі зберігаються в шафі","moreMath":"Чим більше математичних завдань ти виконаєш, тим більше отримаєш коштовностей та енергії лайків"}},"menu":{"mathTopics":"Уся математика","bootcamp":"Bootcamps","dashboard":"Додому","digitalTools":"Цифрові засоби","drillhefter":"Основи математики","encyclopedia":"Енциклопедія","exams":"Eksamensoppgaver","exitPreview":"Закрити попередній перегляд","games":"Ігри","logOut":"Вийти","login":"Увійти","mathEssentials":"Основи математики","mathVault":"Джуніор-матем","register":"Зареєструватися","settings":"Налаштування","studyTips":"Поради з навчання","toggleNavigationMenu":"Перемкнути меню навігації","tutors":"Tutor-on-Demand","daysStreak":"{{days}} днів з реєстрації","learningTools":"Навчальні матеріали","moreLearningTools":"Більше навчальних матеріалів","penNPaperExercise":"Вправи з ручкою та папером","excelOrGeoGebra":"Рецепти Excel / GeoGebra","numberNQuantities":"Числа та величини","statNProbability":"Статистика та ймовірність","stackNLoad":"Stack n´load","juniorMath":"Джуніор-матем","windSurfer":"Wind Surfer","treasureTrail":"Treasure Trail","multiplicationMaster":"Multiplication Master","misc":"Профіль","showMore":"Показати більше","showAllGames":"Показати всі ігри","gotoGames":"Перейти до ігор","switchProfile":"Перемкнути профіль","createFamily":"Додати профіль","getHomApp":"Завантажте додаток House of Math","tryFree":"Спробуйте безкоштовно","signUpForFree":"Зареєструватися безплатно","referral":"Запросити друзів"},"navbar":{"explore":"Ознайомитися","menu":"Меню","panelAdmin":"Панель адміністратора","panelTutor":"Панель репетитора","panelStudent":"Учнівська панель","search":"Пошук","languages":"мова","norwegian":"Norsk","english":"English","ukrainian":"Українська","settings":"Налаштування","logOut":"Вийти","dashboard":"Додому","chat":"Чат","userProfile":"Профіль","leaderboard":"Список лідерів"},"notFound":{"clickOne":"Клацни людину, яку, на твою думку, варто звільнити","fire":"Звільнити","goDashboard":"Перейти до панелі керування","pageNotFound":"Сторінку не знайдено","pageRemoved":"Сторінку видалено","punishDevs":"Наших розробників потрібно покарати за це жахливе недбальство","employeesOnLunchBreak":"Здається, наші співробітники пішли на обідню перерву. Ми незабаром повернемося!"},"search":{"adaptedView":"Індивідуальний режим перегляду","bootcamp":"Bootcamps","all":"Усе","drill":"Основи математики","encyclopedia":"Енциклопедія","noResult":"Результатів пошуку не знайдено","readMore":"Дізнатися більше","watchVideo":"Дивитися відео","remove":"Видалити","search":"Пошук..","geogebra":"GeoGebra","searchResultAppear":"Тут з’являться ваші результати пошуку","searchTooltip":"Індивідуальний режим перегляду призначений для перегляду статей рівня, який ти обрав/обрала у налаштуваннях. Перемкни, щоб переглядати всі статті.","software":"Цифрові засоби","title":"Результати пошуку","searchPlaceholderText":"Чого тобі хочеться вивчити?"},"dashboard":{"activity":"Набір завдань","bootcamp":{"buttonContinueLearning":"Продовжити навчання","buttonToOverview":"Перейти до огляду","comingSoon":"Незабаром!","edit":"Редагувати","title":"Мої Bootcamps"},"gamification":{"badge":"Значок Bootcamp","badgeBackground":"Фон бейджа","buttonToBase":"Схованка","gemIcon":"Коштовності Значок","completeQuestsGetTopics":"Виконай тести, щоб отримати доступ до більшої кількості тем"},"completeProfile":{"button":"Завершити реєстрацію","description":"Нам потрібно дізнатися про тебе трохи більше, щоб персоналізувати твій досвід"},"continue":"Продовжити","topicOverview":"Огляд теми","tutor":{"assigningTutor":"Будь ласка, зачекай, доки ми знайдемо для тебе репетитора.","bookPrivateTutoring":"Замовити репетиторство","tutorPending":"Очікуй","tutorScheduling":"Коли тобі буде призначене заняття, воно з’явиться тут.","myTutor":"Мій репетитор","myTutors":"Мої репетитори","myStudentPanel":"Моя учнівська панель"},"activities":"Завдання","myActivities":"Мої завдання","tagNew":"новий","news":{"buttonChat":"Чат","buttonPlay":"Грати","buttonShowMe":"Покажи мені","buttonStart":"Розпочати","campAlt":"Зона Bootcamps","content1":"Долучайся до пригод разом із бджілкою Д’Рілло за допомогою оновленого розділу Основи математики. Дізнайся про найважливіші математичні теми, граючи з веселими завданнями!","content2":"Наші репетитори готові тобі допомогти. Скористайся чатом, щоб отримати відповіді на всі свої запитання з математики.","content3":"Візьми участь у Чемпіонаті з множення, змагайся з іншими та вигравай першокласні призи!","content4":"Bootcamps — це веселі, інтерактивні, анімовані уроки з математики в ігровій формі для всіх.","content5":"Отримай миттєву допомогу з математики! Замов 15-хвилинне відеозаняття з репетитором.","header1":"Стань майстром математичного вишколу","header2":"Зруш з місця","header3":"Виграй iPad та інші чудові призи ","header4":"Спробуй Bootcamps","header5":"Відеочат ","subject1":"Дроби","title":"Новини"},"newsInHomebase":"Новини на домашній базі","metaDescription":"Уся необхідна тобі допомога з математики безплатно! Отримай повний навчальний план із математики разом із навчальними відео, інтерактивним розв’язуванням завдань, іграми та цілодобовим чатом.","takeQuiz":"Пройти тест","tipOftheDay":"ПОРАДА ДНЯ","doMath":"Зайнятися математикою","doMathLT":"Займайся математикою!","learningPath":"Шлях навчання","learningPathTutorial":{"step1":{"title":"Ми створили твій \u003cspan\u003eшлях навчання\u003c/span\u003e на підставі твоїх відповідей.","action":"Далі"},"step2":{"title":"Щоб пройти рівень, переглянь \u003cspan\u003eвідео\u003c/span\u003e та виконай \u003cspan\u003eзавдання\u003c/span\u003e","action":"Дізнатися більше"},"step3":{"title":"Оціни свої знання,\u003cbr /\u003e взявши участь у \u003cspan\u003eбитві з босом\u003c/span\u003e","action":"Далі!"},"step4":{"title":"Ви завжди можете отримати нові завдання, оновивши ваш \u003cspan\u003eшлях навчання\u003c/span\u003e.","action":"Далі"},"step5":{"title":"Щоб ознайомитися з усіма нашими матеріалами, відвідай розділ \u003cspan\u003eУся математика\u003c/span\u003e","action":"Закінчити"}},"curriculumTutorial1":{"step1":{"title":"Кожна академічна шапочка \u003cCapImage /\u003e позначає математичну тему. Щоб вивчити предмет, потрібно зібрати їх усі","action":"Далі"},"step2":{"title":"Як тільки ти збереш усі шапочки, це означатиме \u003cCapImage /\u003e, що в тебе є знання з {{subjectLabel}}, і ти можеш отримати сертифікат про це","action":"Далі"},"step3":{"title":"ут ти завжди можеш створити свій особистий Навчальний план для найефективнішого способу вивчення математики","action":"зрозумів"}},"curriculumTutorial2":{"step1":{"title":"Кожна частина \u003cPuzzleImage /\u003e являє собою математичну тему. Щоб відкрити скриню з бонусами \u003cChest /\u003e, потрібно зібрати їх усі ","action":"Далі"},"step2":{"title":"Після того, як ти збереш усі частини пазла \u003cPuzzleImage /\u003e, можна почати вивчати {{subjectLabel}} та збирати шапочки. \u003cCapImage /\u003e","action":"Далі"},"step3":{"title":"Коли всі шапочки  \u003cCapImage /\u003e будуть зібрані, це означатиме, що в тебе є знання з {{subjectLabel}}, і ти можеш отримати сертифікат про досягнення","action":"зрозумів"}},"avatarTutorial":{"step1":{"title":"Щоб \u003cspan\u003eстворити свій аватар\u003c/span\u003e, натисни тут","action":"Закінчити"}},"learningPathCardTutorial":{"step1":{"title":"Щоб отримати власний \u003cspan\u003eшлях навчання\u003c/span\u003e, натисни на кнопку","action":"OK"}},"mathTask":{"step1":{"title":"Щоб виконати \u003cspan\u003eматематичне завдання\u003c/span\u003e, \u003cspan\u003eздолай Боса буткемпів!\u003c/span\u003e","action":"Ok"}},"step":"Крок","yourPath":"Твій шлях навчання","latestActivities":"Останні відвідані","activitiesSubtitles":{"multgame":"Останній режим","stacknload":"Останній рівень","treasureTrail":"Останній рівень","windSurfer":"Останній рахунок"},"activitiesShownHere":"Тут буде показано останні відвідані тобою сторінки","checkOutMath":"Ознайомся з певними нашими математичними темами","title":"Панель керування","toolTip":"Огляд твоїх успіхів і навчального шляху.","userCard":{"quizMessageButton":"Тест","quizMessageText":"Високий рівень математичних знань дасть тобі більше можливостей у майбутньому. Чим краще ти знатимеш математику, тим більше варіантів отримаєш. Так що наберися сміливості та берися за математику! Почни з проходження тесту!","quizMessageTitle":"Тест на встановлення відповідності","youHaveNews":"Є новини для тебе! \u003copenHomebase\u003eOpen homebase\u003c/openHomebase\u003e"},"chatBetweenUserAndTutor":"Чат між користувачем і репетитором","imageAlt":{"background":"Зелене бобове стебло з безліччю листя, що різко скручується","homebasePlaceholder":"Логотип House of Math з анімованими зображеннями людей зверху","backgroundMobileTop":"Бобове стебло","backgroundMobileBottom":"Бобове стебло"},"featureProducts":{"label":"Дізнайся про наші галузі знань"},"statistics":{"label":"успіхи","activity":{"label":"Виконані завдання","correct":"Правильні","inCorrect":"Неправильні","instruction":"Щоб розблокувати цю статистику, спробуй наші продукти"},"timeSpent":{"label":"Проведений час","days":"Днів","hours":"Годин","minutes":"Хвилин"},"feedback":{"yes":"Так","no":"Ні","instruction":"Чи бажаєш ти бачити більше статистики в майбутньому?"}},"checklists":{"title":"Розпочати","completeChecklist":"Заповни контрольний список","description":"Заповни контрольний список й отримай нагороду","seeMore":"Побачити більше","close":"Закрити","onboarding":"Отримай свій власний Шлях навчання!","createAvatar":"Створити аватар","exploreSpace":"Відвідати свою схованку","mathTask":"Виконати математичне завдання","exploreLeaderboard":"Завітай до ліги","verifyEmail":"Підтвердити електронну пошту","completeProfile":"Заповнити профіль","mathTaskBadge":"Здолай боса буткемпів","tooltip":{"onboarding":"\u003cstrong\u003eВиконай\u003c/strong\u003e діагностичний тест i \u003cstrong\u003eздобудь {{rewardXP}}{{comma}}{{rewardGems}}.\u003c/strong\u003e","createAvatar":"\u003cstrong\u003eСтвори\u003c/strong\u003e свій особистий аватар і \u003cstrong\u003eздобудь {{rewardXP}}{{comma}}{{rewardGems}}.\u003c/strong\u003e","exploreSpace":"Ознайомся зі своєю \u003cstrong\u003eСхованкою\u003c/strong\u003e і \u003cstrong\u003eздобудь 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Students in Texas, Virginia, Alaska, and Nebraska can also achieve strong learning outcomes with House of Math, but should use the our AI Oracle to ensure they cover all required topics. The platform supports all K–12 math globally, as well as selected university-level subjects.","cancelAnytime":"Yes. You can cancel whenever you want, and you'll keep access until the end of your current billing period. No hidden fees.","gradeLevelsCover":"We cover the full K–12 U.S. curriculum. Lessons are reviewed and verified by expert educators.","freeTrial":"Yes, we offer a 7 day free trial. Cancel anytime during the trial and you won't be charged."}}}},"getStartedV2":{"freeTakes90Seconds":"Free · Takes 90 seconds","understandChildMath":"Let's understand what's happening with your child’s math","answerQuestions":"Answer a few quick questions about what you're seeing at home. 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The real cause is usually a few missing foundational blocks that quietly make every lesson feel scary. House of Math finds exactly which blocks need rebuilding.","ES_EMO_NEW":"Seeing your child shrink away from math is heartbreaking, especially this young. When {{breakdown}} starts to feel scary, it often traces back to a few foundational blocks that never fully solidified — not to lack of effort. House of Math finds exactly which blocks are missing and rebuilds them.","ES_ACA_EXP":"You've already invested in outside support — yet progress in {{breakdown}} hasn't matched the effort. More hours rarely fixes this; finding the specific foundational blocks your child skipped does. House of Math identifies exactly those gaps and rebuilds them.","ES_ACA_NEW":"Early math foundations shape everything that comes later, so wanting your child to do well now is exactly the right instinct. When {{breakdown}} feels harder than it should, the cause is almost never effort — it's a few foundational blocks that didn't fully land. House of Math finds and rebuilds exactly those blocks.","ES_DIA_EXP":"You can tell something isn't working — even after trying outside help — but pinpointing what is harder than people admit. At this age, vague struggles almost always trace back to a few specific foundational blocks, often around {{breakdown}}. House of Math diagnoses exactly which blocks need attention and rebuilds them.","ES_DIA_NEW":"Sensing something is off — without knowing exactly what — is actually the most useful starting point. At the elementary level, vague struggles almost always come down to a few specific foundational blocks, often around {{breakdown}}. House of Math diagnoses exactly which blocks need rebuilding.","MS_EMO_EXP":"Middle school is when math anxiety hits hardest, and the extra support you've given hasn't fully reached the stress around {{breakdown}}. The pressure usually isn't about middle school content itself — it builds on earlier foundational blocks that never fully solidified. House of Math finds and rebuilds exactly those blocks, so confidence can return.","MS_EMO_NEW":"Math pressure peaks in middle school, and seeing your child shut down around {{breakdown}} is genuinely hard to watch. This anxiety almost never starts in middle school — it builds on earlier foundational blocks that quietly never solidified. House of Math finds those exact missing blocks and rebuilds them, clearing the anxiety at its source.","MS_ACA_EXP":"You've invested real time and outside support in your child's math — yet {{breakdown}} still feels harder than it should. That's not a sign of insufficient effort; it's a signal that earlier foundational blocks have gaps. House of Math finds exactly which blocks are missing and rebuilds them, so the hours invested finally translate into progress.","MS_ACA_NEW":"Middle school is a critical window — what gets solid now shapes high school and beyond. If {{breakdown}} is harder than it should be, the cause is usually a few earlier foundational blocks that didn't fully form, not effort. House of Math finds exactly those blocks and rebuilds them before middle school content can fully click.","MS_DIA_EXP":"You've tried outside help, yet something still feels off — even if you can't name exactly what. Middle school struggles almost always trace back to specific foundational blocks from earlier years, often surfacing around {{breakdown}}. House of Math diagnoses exactly which blocks are missing and rebuilds them.","MS_DIA_NEW":"Knowing something is off — without being able to pinpoint what — is actually a clear-eyed read. Middle school difficulties almost always trace back to specific foundational blocks from earlier years, often around {{breakdown}}. House of Math diagnoses exactly which blocks need rebuilding before they compound further.","HS_EMO_EXP":"High school math anxiety is uniquely heavy — grades feel permanent, and the extra support you've provided hasn't eased the stress around {{breakdown}}. High school content sits on years of earlier foundational blocks, and gaps from before are usually what's driving the anxiety now. House of Math finds those exact missing blocks and rebuilds them.","HS_EMO_NEW":"By high school, math anxiety carries real weight — grades and college pressure feed it, especially around {{breakdown}}. Pushing harder rarely helps now; the anxiety usually traces back to foundational blocks from earlier years that quietly never solidified. House of Math finds those exact blocks and rebuilds them, clearing the source of the stress.","HS_ACA_EXP":"You've invested seriously in outside support — yet {{breakdown}} still feels harder than the effort warrants. With high school stakes this high, that gap is worth taking seriously: it almost always traces to earlier foundational blocks that never fully solidified. House of Math finds those exact blocks and rebuilds them, so your child's effort finally compounds.","HS_ACA_NEW":"High school math determines real outcomes — GPA, college options. If {{breakdown}} is harder than it should be, the cause is rarely effort; high school content stacks on years of earlier foundational blocks, and gaps from before make advanced topics feel impossible. House of Math finds and rebuilds those missing blocks before the gap widens.","HS_DIA_EXP":"Knowing something is off — despite the outside help you've sought — is a more accurate read than most parents credit themselves for. 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