Answer
$2\log_4{x}+3\log_4{y}$
Work Step by Step
RECALL:
(1) Product Property of Logarithms:
$\log_a{mn}=\log_a{m} + \log_a{n}$
(2) Quotient Property of Logarithms:
$\log_a{\frac{m}{n}}=\log_a{m} - \log_a{n}$
(3) Power Property of Logarithms:
$\log_a{m^n}=n\log_a{m}$
Use the Product Property to obtain:
$$\log_4{x^2y^3}=\log_4{x^2}+\log_4{y^3}$$
Use the Power Property to obtain:
$$\log_4{x^2}+\log_4{y^3}=2\log_4{x}+3\log_4{y}$$
