# How do you evaluate f(x)=log_16x for x=4?

Aug 1, 2017

log_16(4) = color(blue)(1/2

#### Explanation:

${\log}_{16} \left(4\right)$

This can also be written as

${16}^{x} = 4$

We know that $4$ is the square root of $16$, so

$4 = {16}^{1 \text{/} 2}$

(which is equivalent to $\sqrt{16} = 4$)

Therefore,

log_16(4) = color(blue)(1/2