Simplify/Condense 2/3 log base 2 of x-3 log base 2 of y

$\frac{2}{3} \log_{2} (x) - 3 \log_{2} (y)$

Simplify each term.

Simplify $\frac{2}{3} \log_{2} (x)$ by moving $\frac{2}{3}$ inside the logarithm.

$\log_{2} (x^{\frac{2}{3}}) - 3 \log_{2} (y)$

Simplify $- 3 \log_{2} (y)$ by moving $3$ inside the logarithm.

$\log_{2} (x^{\frac{2}{3}}) - \log_{2} (y^{3})$

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

$\log_{2} (\frac{x^{\frac{2}{3}}}{y^{3}})$