Answer
1.146
Work Step by Step
Using the properties of logarithms, the given expression, $
\log_a 14
,$ is equivalent to
\begin{align*}
&
\log_a [2(7)]
\\&=
\log_a 2+\log_a 7
&(\log (xy)=\log x+\log y)
.\end{align*}
Using the given values, $
\log_a 2=0.301
$ and $
\log_a 7=0.845
,$ the expression above becomes
\begin{align*}
&
0.301+0.845
\\&=
1.146
.\end{align*}
Hence, the given expression evaluates to $
1.146
$.
