Answer
$\frac{1}{3}$
Work Step by Step
We know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (where $x\gt0$, $b\gt0$, and $b\ne1$).
Also, based on the definition of the common logarithm, we know that $log(x)=log_{10}x$.
Therefore, $log\sqrt[3] 10=log_{10}\sqrt[3] 10=\frac{1}{3}$, because $10^{\frac{1}{3}}=\sqrt[3] 10$.
