Answer
$4C$
Work Step by Step
Note that $81=3^4$.
Thus, the given expression is equivalent to:
$=\log_b{(3^4)}$
RECALL:
(1) $\log_b{(\frac{m}{n})} = \log_b{m} - \log_b{n}$
(2) $\log_b{mn} = \log_b{m} + \log_b{n}$
(3) $\log_b{(m^n)} = n \cdot \log_b{m}$
Use rule (3) above to obtain:
$=4\log_b{3}$
With $\log_b{2} = A$ and $\log_b{3}=C$, the expression above is equivalent to:
$=4C$
