# How do you evaluate log_216 6?

${\log}_{216} 6 = \frac{1}{3}$

#### Explanation:

A couple of things to know/remember to answer this:

${\log}_{216} 6$ is asking how many times 216 needs to be multiplied by itself in order to arrive at 6. Clearly the answer is less than 1!

${216}^{\frac{1}{2}}$ is the same as $\sqrt{216}$. ${216}^{\frac{1}{3}}$ is the same as $\sqrt[3]{216}$. And so on.

Ok... what is ${\log}_{216} 6$?

One way to do this is to work from the 6 to the 216 - it turns out that:

${6}^{3} = 216$

Which means that

${216}^{\frac{1}{3}} = 6$

and so:

${\log}_{216} 6 = \frac{1}{3}$