# How do you calculate Log_5 77?

Jun 9, 2016

${\log}_{5} 77 = \frac{\log 77}{\log 5} \approx 2.698958$

#### Explanation:

If you have a calculator which can calculate natural or common logs, then you can make use of the change of base formula:

${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$

So in our example, you might use:

${\log}_{5} 77 = \frac{\log 77}{\log 5} \approx \frac{1.88649}{0.69897} \approx 2.698957$

Or with natural logarithms:

${\log}_{5} 77 = \frac{\ln 77}{\ln 5} \approx \frac{4.3438054}{1.6094379} \approx 2.698958$