Answer
$\log_2 a - 2\log_2 b$
Work Step by Step
Recall:
$\log_a\left(\dfrac{M}{N}\right) = \log_a M-\log_a N$
Using the rule above gives;
$\log_2 \left(\dfrac{a}{b^2} \right) = \log_2 a-\log_2 b^2$
Note that $\log_a M^r = r \log_a M$
Therefore, the expression above simplifies to:
$\log_2 \left(\dfrac{a}{b^2} \right) = \boxed{\log_2 a - 2\log_2 b}$
