Answer
$\approx1.9376$
Work Step by Step
Using $\log_a b=\dfrac{\log b}{\log a}$ or the Change-Of-Base Theorem, the given expression, $
\log_{\sqrt{13}} 12
,$ evaluates to
\begin{array}{l}\require{cancel}
\dfrac{\log 12}{\log \sqrt{13}}
\\\\
\approx1.9376
.\end{array}