Answer
$\log_2{a}-2\log_2{b}$
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) above to obtain:
$\log_2 {\frac{a}{b^2}}=\log_2{a}-\log_2{b^2}$.
Use Rule (2) above to obtain:
$\log_2{a}-\log_2{b^2}=\log_2{a}-2\log_2{b}$
