# How do you simplify log_2 8?

May 23, 2016

First use the change of base rule ${\log}_{n} a = \log \frac{a}{\log} n$

#### Explanation:

$= \log \frac{8}{\log} 2$

$= \log \frac{{2}^{3}}{\log} 2$

By the rule $\log {n}^{a} = a \log n$

$= \frac{3 \log 2}{\log} 2$

$= 3$

Hopefully this helps.