Answer
$\frac{1}{3}\log{x} - \frac{1}{3}\log{y}$
Work Step by Step
Note that $\sqrt[3]{\frac{x}{y}} = \left(\frac{x}{y}\right)^{\frac{1}{3}}$ therefore the expression above is equivalent to:
$=\log{(\frac{x}{y})^{\frac{1}{3}}}$
RECALL:
(1) $\log{(b^c)}=c \cdot \log{b}$
(2) $\log{(xy)} = \log{x} + \log{y}$
(3) $\log{(\frac{x}{y})}=\log{x} - \log{y}$
Use rule (1) above to obtain:
$=\frac{1}{3}\log{(\frac{x}{y})}$
Use rule (3) above to obtain:
$=\frac{1}{3}(\log{x} - \log{y})
\\=\frac{1}{3}\log{x} - \frac{1}{3}\log{y}$
