Simplify/Condense 1/3*( log base 2 of x- log base 2 of y)

$\frac{1}{3} \cdot (\log_{2} (x) - \log_{2} (y))$

Step 1

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

$\frac{1}{3} \cdot \log_{2} (\frac{x}{y})$

Step 2

Simplify $\frac{1}{3} \log_{2} (\frac{x}{y})$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{2} ({(\frac{x}{y})}^{\frac{1}{3}})$

Step 3

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

$\log_{2} (\frac{x^{\frac{1}{3}}}{y^{\frac{1}{3}}})$