Answer
$x=2$
Work Step by Step
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x$ and every real number $y$.
Therefore, $log_{8}x=\frac{1}{3}$ is equivalent to $8^{\frac{1}{3}}=x$.
We know that $x=2$, because $8^{\frac{1}{3}}=\sqrt[3] 8=2$.
