jmc

We set ${\log }_{\sqrt[3]{5}}125=x$, so we have ${\sqrt[3]{5}}^x=125$. Expressing both sides as powers of $5$, we have $(5^{\frac{1}{3}}{)}^x=5^3$, or $5^{\frac{x}{3}}=5^3$. Thus $\frac{x}{3}=3$ and $\boxed{x=9}$.