Write as a Single Logarithm 7 log base 2 of x-1/3 log base 2 of y

$7 \log_{2} (x) - \frac{1}{3} \log_{2} (y)$

Step 1

Simplify each term.

Simplify $7 \log_{2} (x)$ by moving $7$ inside the logarithm.

$\log_{2} (x^{7}) - \frac{1}{3} \cdot \log_{2} (y)$

Multiply $- \frac{1}{3} \log_{2} (y)$ .

Reorder $\log_{2} (y)$ and $\frac{1}{3}$ .

$\log_{2} (x^{7}) - (\frac{1}{3} \log_{2} (y))$

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

$\log_{2} (x^{7}) - \log_{2} (y^{\frac{1}{3}})$

Step 2

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

$\log_{2} (\frac{x^{7}}{y^{\frac{1}{3}}})$