Answer
$\log_5{x^9}$
Work Step by Step
RECALL:
(1) $\log_b{m} - \log_b{n} = \log_b{(\frac{m}{n})}$
(2) $\log_b{m} + \log_b{n} = \log_b{(mn)}$
(3) $n \cdot \log_b{m} = \log_b{(m^n)}$
Use rule (3) above to obtain:
$=\log_5{(x^7)} + \log_5{(x^{2})}$
Use rule (2) above to obtain:
$=\log_5{(x^7 \cdot x^2)}
\\=\log_5{x^9}$
