# How do you evaluate log_16 8?

Feb 20, 2017

${\log}_{16} 8 = \frac{3}{4}$

#### Explanation:

Let ${\log}_{16} 8 = x$, then from definition of logarithm,

${16}^{x} = 8$

or ${\left({2}^{4}\right)}^{x} = {2}^{3}$

or ${2}^{4 x} = {2}^{3}$

or $4 x = 3$

i.e. $x = \frac{3}{4}$

Hence ${\log}_{16} 8 = \frac{3}{4}$