Answer
$x=\frac{1}{2}$
Work Step by Step
We know that if $\log_a{y}=x$ then $a^x=y$.
Hence, if $\log_x{\left(\frac{1}{8}\right)}=3$, then
$x^3=\frac{1}{8}$
Solve the equation above to obtain:
$x^3=\left(\frac{1}{2}\right)^3\\
\sqrt[3]{x^3}=\sqrt[3]{\left(\frac{1}{2}\right)^3}\\
x=\frac{1}{2}$.