# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_3 10.741?

Sep 23, 2015

I found: $2.16097$
Given a log in base $b$ of a certain number $a$ you can change it into the new base $c$ as:
${\log}_{b} a = \frac{{\log}_{c} a}{{\log}_{c} b}$
A convenient base we can use in our case is $e$, to get natural logs indicated as $\ln$ and that can be evaluated using a pocket calculator. So we get:
${\log}_{3} \left(10.741\right) = \frac{\ln \left(10.741\right)}{\ln \left(3\right)} = 2.16097$