Answer
$2\log{z}-\log{5}$
Work Step by Step
RECALL:
(1) Product Property of Logarithms:
$\log_a{mn}=\log_a{m} + \log_a{n}$
(2) Quotient Property of Logarithms:
$\log_a{\frac{m}{n}}=\log_a{m} - \log_a{n}$
(3) Power Property of Logarithms:
$\log_a{m^n}=n\log_a{m}$
Use the Quotient Property to obtain:
\begin{align*}
\log{\frac{z^2}{5}}&=\log{z^2}-\log{5}\\
\end{align*}
Use the Power Property to obtain:
$$\log{z^2} - \log{5}=2\log{z}-\log{5}$$
