Answer
$3\log_2{x}-\log_2{(x-3)}.$
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) to obtain
$\log_2{\frac{x^3}{x-3}}=\log_2{x^3}-\log_2{(x-3)}$.
Use Rule (2) to obtain
$\log_2{x^3}-\log_2{(x-3)}=3\log_2{x}-\log_2{(x-3)}.$
