Expand log base a of x^3y^5

$\log_{a} (x^{3} y^{5})$

Rewrite $\log_{a} (x^{3} y^{5})$ as $\log_{a} (x^{3}) + \log_{a} (y^{5})$ .

$\log_{a} (x^{3}) + \log_{a} (y^{5})$

Expand $\log_{a} (x^{3})$ by moving $3$ outside the logarithm.

$3 \log_{a} (x) + \log_{a} (y^{5})$

Expand $\log_{a} (y^{5})$ by moving $5$ outside the logarithm.

$3 \log_{a} (x) + 5 \log_{a} (y)$

Expand log base a of x^3y^5