Mathematics: Consider the equation below. log4 (x+3)=log2 (2x). which system of equations can represent the equation?

Consider the equation below. log4 (x+3)=log2 (2x).

Ответ:

weeblordd

12.03.2022

Note that
$log_{4} (x+3) = \frac{log_{2} (x+3)}{log_{2}4}$

Therefore, given
log₄(x+3) = log₂(2x), obtain
$\frac{log_{2}(x+3)}{log_{2}4}=log_{2} (2x) \\ log_{2}(x+3) = log_{2}4 log_{2}(2x) \\ x+3 = (2x)^{log_{2}4}$
Because
log₂4 = log₂ 2² = 2 log₂ 2 = 2, therefore
x + 3 = (2x)² = 4x²
4x² - x - 3 = 0
This factorizes into
(4x + 3)(x - 1) = 0

4x² - x - 3 = 0
or
4x + 3 = 0, and
x - 1 = 0

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Ответ:

jdobes9578

13.09.2021

Mathematics

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Consider the equation below. log4 (x+3)=log2 (2x). which system of equations can represent the equation?

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