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Answer 1 · 2017-05-08T12:28:01

$x=6/5$

We have:

$25^(2x) = 125^(3x-2)$

Taking logarithms we have:

$log(25^(2x)) = log(125^(3x-2))$

We will use some properties of logarithms we have:

$log (a^b) = bloga$

Applying we get:

$2xlog25 = (3x-2)log125$

$:. 2xlog5^2 = (3x-2)log5^3$
$:. 4xlog5 = 3(3x-2)log5$
$:. 4x = 3(3x-2)$
$:. 4x = 9x - 6$
$:. 5x=6$
$:. x=6/5$