Simplify/Condense 1/3( log of x- log of y)

$\frac{1}{3} (\log (x) - \log (y))$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\frac{1}{3} \cdot \log (\frac{x}{y})$

Simplify $\frac{1}{3} \log (\frac{x}{y})$ by moving $\frac{1}{3}$ inside the logarithm.

$\log ({(\frac{x}{y})}^{\frac{1}{3}})$

Apply the product rule to $\frac{x}{y}$ .

$\log (\frac{x^{\frac{1}{3}}}{y^{\frac{1}{3}}})$