Answer
$\log_3{x}-2$
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 (4) above to obtain:
$\log_3 {\frac{x}{9}}=\log_3 {x}-\log_3 {9}.$
Use Rule (2) above to obtain:
$\log_3 {x}-\log_3 {9}\\
=\log_3 {x}-\log_3 {3^2}\\
=\log_3 {x}-2\cdot \log_3 {3}\\
=\log_3{x}-2\cdot1\\
=\log_3{x}-2$
