Answer
The equivalent expression for $\frac{1}{2}\log a-\log b-2\log c$ is $\log \frac{\sqrt{a}}{b{{c}^{2}}}$.
Work Step by Step
$\frac{1}{2}\log a-\log b-2\log c$
Apply the power rule for logarithms and simplify the expression as follows.
$\frac{1}{2}\log a-\log b-2\log c=\log {{a}^{\frac{1}{2}}}-\left( \log b+\log {{c}^{2}} \right)$
Apply the product rule as follows.
$\frac{1}{2}\log a-\log b-2\log c=\log {{a}^{\frac{1}{2}}}-\log b{{c}^{2}}$
Apply the quotient rule as follows.
$\begin{align}
& \frac{1}{2}\log a-\log b-2\log c=\log \frac{{{a}^{\frac{1}{2}}}}{b{{c}^{2}}} \\
& =\log \frac{\sqrt{a}}{b{{c}^{2}}}
\end{align}$
