Answer
$\log_3{x} - 2$
Work Step by Step
RECALL:
(1) $\log_a{(MN)} = \log_a{M} + \log_a{N}$
(2) $\log_a{\left(\dfrac{M}{N}\right)} = \log_a{M} - \log_a{N}$
(3) $\log_a{a} = 1$
Note that $9=3(3)$. So the given expression is equivalent to:
$\log_3{\left(\dfrac{x}{3\cdot3}\right)}$
Using rule (2) above, the given expression is equivalent to:
$=\log_3{x} - \log_3{(3 \cdot 3)}$
Using rule (3) above, the expression is equivalent to:
$=\log_3{x} - \left(\log_3{3}+\log_3{3}\right)$
Using rule (3) above, the expression above simplifies to:
$=\log_3{x} - (1+1)
\\=\log_3{x} - 2$
