Answer
$-3\log_2{x}$
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(3) above to obtain:
$\log_2{(\frac{1}{x})}+\log_2{(\frac{1}{x^2})}\\
=\log_2{\left(\frac{1}{x}\cdot \frac{1}{x^2}\right)}\\
=\log_2{(\frac{1}{x^3})}$
Use the rule $\frac{1}{a^m}=a^{-m}$ to obtain
$\log{\left(\frac{1}{x^3}\right)}=\log_2{\left(x^{-3}\right)}$
Use Rule(2) above to obtain:
$\log_2{x^{-3}}=-3\log_2{x}$
