Answer
$\log_4{(x^5)}$
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 Power Property to obtain:
$$3\log_4{x}+2\log_4{x}=\log_4{x^3}+\log_4{x^2}$$
Use the Product Property to obtain:
$$\log_4{x^3}+\log_4{x^2}=\log_4{(x^3\cdot x^2)}=\log_4{x^5}$$
