Answer
$\log_5{3} + 2\log_5{x}-3\log_5{y}$
Work Step by Step
RECALL:
(1) $\log_b{(PQ)} = \log_b{P} + \log_b{Q}$
(2) $\log_b{(\frac{P}{Q})} = \log_b{P} - \log_b{Q}$
(3) $\log_b{(x^n)}=n(\log_b{x})$
Use rule (2) above to obtain:
$=\log_5{(3x^2)} - \log_5{(y^3)}$
Use rule (1) above to obtain:
$=\log_5{3} + \log_5{(x^2)} -\log_5{(y^3)}$
Use rule (3) above to obtain:
$=\log_5{3} + 2\log_5{x}-3\log_5{y}$
