Answer
$\log_5{(u^3 v^4)}$
Work Step by Step
Recall:
$\because \log_a M^r = r \log_a M$
Use the rule above to obtain:
$3 \log_5 u = \log_5 u^3$
$4 \log_5 v = \log_5 v^4$
Thus,
$3 \log_5 u + 4 \log_5 v = \log_5 u^3 +\log_5 v^4$
Recall also that:
$\log_a (MN) = \log_a M+\log_a N$
Using the rule above gives:
$\log_5 u^3 +\log_5 v^4 = \log_5{(u^3 v^4)}$
Therefore,
$3 \log_5 u + 4 \log_5 v = \boxed{\log_5{(u^3 v^4)}}$
