# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_2 12?

Jun 20, 2015

${\log}_{2} \left(12\right) = 3.585$

#### Explanation:

You can convert your log into natural log, $\ln$ (that can evaluated using a calculator) using the change of base as:
${\log}_{a} b = {\log}_{c} \frac{b}{\log} _ c a$

${\log}_{2} \left(12\right) = \ln \frac{12}{\ln} \left(2\right) = 3.585$

You can check the result by doing: ${2}^{3.585} = 12$