# 3log_8(512^{x^{2}})=36 Find x

$3{\mathrm{log}}_{8}\left({512}^{{x}^{2}}\right)=36$
Find x
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joshyoung05M

Divide both sides by 3
${\mathrm{log}}_{8}\left({512}^{{x}^{2}}\right)=12$
Write in expinential form: ${\mathrm{log}}_{b}a=x\to {b}^{x}=a$
${8}^{1}2={512}^{x}$
Since ${8}^{3}=512$, we can write
${8}^{1}2=\left({8}^{3}{\right)}^{\left(}{x}^{2}\right)$
${8}^{1}2={8}^{3{x}^{2}}$
Equate exponens
$12=3{x}^{2}$
$4={x}^{2}$
$x=2x=-2$