#### Answer

$\log_{4}40=\dfrac{\ln40}{\ln4}\approx2.660964$

#### Work Step by Step

$\log_{4}40$
Apply the change of base formula, which is $\log_{b}x=\dfrac{\log_{a}x}{\log_{a}b}$, to express the given $\log$ in terms of the natural logarithm:
$\log_{4}40=\dfrac{\ln40}{\ln4}$
Evaluate using a calculator:
$\dfrac{\ln40}{\ln4}\approx2.660964$