Answer
-3.6602.
Work Step by Step
${{\log }_{a}}\frac{1}{4}$
Apply the quotient rule for logarithms as follows.
$\begin{align}
& {{\log }_{a}}\frac{1}{4}={{\log }_{a}}1-{{\log }_{a}}4 \\
& =0-{{\log }_{a}}{{2}^{2}}
\end{align}$
Apply the power rule as follows.
$\begin{align}
& {{\log }_{a}}\frac{1}{4}=-2{{\log }_{a}}2 \\
& =-2\left( 1.8301 \right) \\
& =-3.6602
\end{align}$
