# How do you evaluate log_6(216)?

If ${\log}_{6} \left(216\right) = x$, we can say that $x = {\log}_{6} \left({6}^{3}\right) = 3 {\log}_{6} \left(6\right) = 3.$
Basically, if you have a logarithm ${\log}_{a} \left(b\right)$, you can ask yourself, "$a$ to WHAT power gives me $b$?"
In this situation, $6$ to the $3 r d$ power will give you $216$, so the answer is $3$.
In situations where the answer won't be an easy integer or fraction, you can input a logarithm in the form ${\log}_{a} \left(b\right)$ in your calculator simply as $\log \frac{b}{\log} a$ in your calculator. You can put $\log \frac{216}{\log} 6$ into your calculator and it will spit out an answer of $3$.