Solve for $x$ , given $x^((log_5 x)-2) = (x^2/(125))$ ?

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Answer 1 · 2017-10-23T14:51:34

$x = {5,125}$

Applying $log_5$ to both sides

$(log_5 x-2)log_5 x=2log_5x - 3$ and now calling $y = log_5 x$

$(y-2)y=2 y-3$ or $y^2-4y+3=0$ now solving for $y$

$y = {1,3}$ or

$log_5 x = 1 rArr x = 5$ and $log_5 x = 3 rArr x = 125$

Solve for xx, given x^((log_5 x)-2) = (x^2/(125))x^((log_5 x)-2) = (x^2/(125)) ?