Question #8d9f9

May 8, 2017

$x = \frac{6}{5}$

Explanation:

We have:

${25}^{2 x} = {125}^{3 x - 2}$

Taking logarithms we have:

$\log \left({25}^{2 x}\right) = \log \left({125}^{3 x - 2}\right)$

We will use some properties of logarithms we have:

$\log \left({a}^{b}\right) = b \log a$

Applying we get:

$2 x \log 25 = \left(3 x - 2\right) \log 125$

$\therefore 2 x \log {5}^{2} = \left(3 x - 2\right) \log {5}^{3}$
$\therefore 4 x \log 5 = 3 \left(3 x - 2\right) \log 5$
$\therefore 4 x = 3 \left(3 x - 2\right)$
$\therefore 4 x = 9 x - 6$
$\therefore 5 x = 6$
$\therefore x = \frac{6}{5}$