Answer
$0.5646$
Work Step by Step
Using $\log_bx=\dfrac{\log x}{\log b}$ or the Change-of-Base Formula, the given expression, $
\log_7 3
,$ is equivalent to
\begin{align*}
&
\dfrac{\log3}{\log7}
.\end{align*}
Using a calculator, with $
\log3\approx0.47712
$ and $
\log7\approx0.84510
$, then
\begin{align*}
\dfrac{\log3}{\log7}&\approx
\dfrac{0.47712}{0.84510}
\\\\&\approx
0.5646
.\end{align*}
Hence, the approximate value of $
\log_7 3
$, is $
0.5646
$.
