# How do you write 9^(-1/2)=1/3 in Log form?

${\log}_{9} \left(\frac{1}{3}\right) = - \frac{1}{2}$

#### Explanation:

First let's remember that:

${x}^{b} = y$ is saying "how many times do we multiply x by itself to arrive at y"

and that in log form, it's

${\log}_{x} y = b$ is saying "b is the number of times we x by itself in order to arrive at y"

So we can convert:

${9}^{- \frac{1}{2}} = \frac{1}{3}$ into

${\log}_{9} \left(\frac{1}{3}\right) = - \frac{1}{2}$