# How do you solve log_8 25= 2log_8 x?

Apr 11, 2016

$x = 5$

#### Explanation:

Rearrange using laws of logarithms, where a coefficient outside a $\log$ is the same as a power inside it.

${\log}_{8} 25 = 2 {\log}_{8} x = {\log}_{8} {x}^{2}$

Raise both sides by eight,

${8}^{{\log}_{8} 25} = {8}^{{\log}_{8} {x}^{2}}$
$25 = {x}^{2}$

which gives $x = - 5 , 5$.

But you can't have a $\log$ of a negative number, which just leaves $5$.