Answer
$\log_5{(u^3v^4)}$
Work Step by Step
Recall:
(1) $\sqrt[m]{a}=a^{\frac{1}{m}}$
(2) $\log_a {x^n}=n\cdot \log_a {x}$.
(3) $\log_a{xy}=\log_a{x} +\log_a{y}$
(4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$
Use Rule (2) above to obtain:
$3\log_5{u}+4\log_5{v}=\log_5{u^3}+\log_5{v^4}$.
Use Rule (3) above to obtain:
$\log_5{u^3}+\log_5{v^4}=\log_5{(u^3v^4)}$
