# How do you calculate log_16 512?

May 21, 2016

${\log}_{16} 512 = \frac{9}{4}$

#### Explanation:

The change of base formula tells us that if $a , b , c > 0$ then:

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

Note that

$16 = {2}^{4}$

$512 = {2}^{9}$

So we find:

${\log}_{16} 512 = \frac{{\log}_{2} 512}{{\log}_{2} 16} = \frac{{\log}_{2} {2}^{9}}{{\log}_{2} {2}^{4}} = \frac{9}{4}$