Answer
$3 \log_2 x- \log_2 (x-3)$
Work Step by Step
Recall that:
$\log_a\left(\dfrac{M}{N}\right) = \log_a M-\log_a N$
Using the rule above gives:
$\log_2 \left(\dfrac{x^3}{x-3} \right) = \log_2{\left(x^3\right)} - \log_2{(x-3)}$
With $\log_a M^r = r \log_a M$, the expressions above simplifies to:
$\log_2 \left(\dfrac{x^3}{x-3} \right) = \boxed{3 \log_2 x- \log_2 (x-3)}$
