Answer
$2.5850$
Work Step by Step
Using $\log_bx=\dfrac{\log x}{\log b}$ or the Change-of-Base Formula, the given expression, $
\log_2 6
,$ is equivalent to
\begin{align*}
&
\dfrac{\log6}{\log2}
.\end{align*}
Using a calculator, with $
\log6\approx0.77815
$ and $
\log2\approx0.30103
$, then
\begin{align*}
\dfrac{\log6}{\log2}&\approx
\dfrac{0.77815}{0.30103}
\\\\&\approx
2.5850
.\end{align*}
Hence, the approximate value of $
\log_2 6
$, is $
2.5850
$.
