Question

помогиие пожалуйста надо решить
${12}^{x} - {4}^{x - 1} \times {3}^{x - 2} = 140$
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Answer 1

$12^x - 4^{x-1}\cdot 3^{x-2} = 140$

$12^x - \frac{4^x}{4}\cdot\frac{3^x}{3^2} = 140$

$12^x - \frac{4^x\cdot 3^x}{4\cdot 9} = 140$

$12^x - \frac{(4\cdot 3)^x}{36} = 140$

$12^x - \frac{12^x}{36} = 140$

$12^x \cdot ( 1 - \frac{1}{36}) = 140$

$12^x \cdot \frac{36-1}{36} = 140$

$12^x \cdot \frac{35}{36} = 140$

$12^x = 140\cdot \frac{36}{35} = 4\cdot 36 = 144 = 12^2$

$12^x = 12^2$

$x = \log_{12}12^2 = 2$.

Ответ. 2.