Question #8d9f9

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Question #8d9f9

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Answer 1 · 2017-05-08T12:28:01

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

Explanation:

We have:

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

Taking logarithms we have:

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

We will use some properties of logarithms we have:

$log (a^{b}) = b log a$ $log (a^b) = bloga$

Applying we get:

$2 x log 25 = (3 x - 2) log 125$ $2xlog25 = (3x-2)log125$

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

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Question #8d9f9

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