# Logarithm question equation I'm stuck on an equation : ( log 8 </msub> &#

Willow Pratt 2022-06-30 Answered
Logarithm question equation
I'm stuck on an equation :
$\left({\mathrm{log}}_{8}x{\right)}^{2}+2{\mathrm{log}}_{8}x+1=0$
I've played with it without any success. Any indications would be greatly appreciated...
Thank you!
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conveneau71
You've got ${u}^{2}+2u+1=0$, where $u={\mathrm{log}}_{8}x$
Factoring, you get $\left(u+1{\right)}^{2}=0$, which entails that $u=-1$
If ${\mathrm{log}}_{8}x=-1$ then ${8}^{-1}=x$, i.e. $x=\frac{1}{8}$