Answer
$\displaystyle \frac{1}{3}\log x-\frac{1}{3}\log y $
Work Step by Step
$\displaystyle \log\sqrt[3]{\frac{x}{y}}=\log(\frac{x}{y})^{1/3}$
$\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\displaystyle \frac{1}{3}(\log\frac{x}{y})\quad $..apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\displaystyle \frac{1}{3}(\log x-\log y)\quad $... distribute
$=\displaystyle \frac{1}{3}\log x-\frac{1}{3}\log y $
