# How do you solve 6^n=99?

Sep 23, 2016

I got: $n = 2.56458$
I would try taking the log in base $6$ of both sides:
${\log}_{6} \left({6}^{n}\right) = {\log}_{6} \left(99\right)$
$n = {\log}_{6} \left(99\right)$
the log is tricky but if we have a calculator we can evaluate it after changing its base, say, to get a natural log in base $e$ indicated as $\ln$. So we get:
$n = \ln \frac{99}{\ln \left(6\right)} = 2.56458$