# How do you evaluate log_16 (1/2)?

May 3, 2018

$- \frac{1}{4}$

#### Explanation:

${\log}_{16} \left(\frac{1}{2}\right) = x$

We know that ${\log}_{b} \left(x\right) = y$ equals to ${b}^{y} = x$. Therefore, we can rewrite it as:
${16}^{x} = \frac{1}{2}$

Make both sides have a base of $2$:
${2}^{4 x} = {2}^{-} 1$

Since both sides have the same base, it becomes:
$4 x = - 1$

Divide both sides by $\textcolor{b l u e}{4}$:
$\frac{4 x}{\textcolor{b l u e}{4}} = - \frac{1}{\textcolor{b l u e}{4}}$

Therefore,
$x = - \frac{1}{4}$

The answer is $- \frac{1}{4}$.

Hope this helps!