Answer
$\log_3{\dfrac{1}{x^{\frac{5}{2}}}}$
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:
$\log_3{\sqrt x}-\log_3{x^3}\\
=\log_3{\frac{\sqrt{x}}{x^3}}\\
=\log_3{\frac{x^{\frac{1}{2}}}{x^3}}\\
=\log_3{\frac{1}{x^{3-\frac{1}{2}}}}\\
=\log_3{\dfrac{1}{x^{\frac{5}{2}}}}$
