# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_4 20?

Jul 2, 2015

I found: ${\log}_{4} \left(20\right) = 2.161$

#### Explanation:

Your formula can be used to convert, for example, to natural log or $\ln$;
you can write:
${\log}_{4} \left(20\right) = \ln \frac{20}{\ln} \left(4\right) =$ and both can be evaluated with a pocket calculator giving:
$= \frac{2.996}{1.386} = 2.161$
Using this value you can check your result as:

${4}^{2.161} = 20$