Answer
8.7601.
Work Step by Step
${{\log }_{a}}28$
Simplify the logarithm as follows.
$\begin{align}
& {{\log }_{a}}28={{\log }_{a}}\left( 4\cdot 7 \right) \\
& ={{\log }_{a}}\left( {{2}^{2}}\cdot 7 \right)
\end{align}$
Apply the product rule for logarithms as follows.
${{\log }_{a}}28={{\log }_{a}}{{2}^{2}}+{{\log }_{a}}7$
Apply the power rule for logarithms as follows.
${{\log }_{a}}28=2{{\log }_{a}}2+{{\log }_{a}}7$
Substitute ${{\log }_{a}}2=1.8301\text{ and }{{\log }_{a}}7=5.0999$.
$\begin{align}
& {{\log }_{a}}28=2\left( 1.8301 \right)+5.0999 \\
& =8.7601
\end{align}$
