Answer
$0.6826$
Work Step by Step
Using $\log_b x=\dfrac{\log x}{\log b}$ or the Change-of-Base Formula, the given expression, $
\log_53
,$ is equivalent to
\begin{align*}
\dfrac{\log3}{\log5}
.\end{align*}
Since the bases of the logarithms are now base-$10$, a calculator can be used to compute the logarithms. That is,
\begin{align*}
\dfrac{\log3}{\log5}
&\approx
\dfrac{0.47712125471966243729502790325512}{0.69897000433601880478626110527551}
\\\\&\approx
0.6826
.\end{align*}
Hence, $\log_53$ is approximately equal to $0.6826$.
