# How do you solve 3^(2x) = 81?

The unique solution is $x = \ln \frac{81}{2 \ln \left(3\right)}$.
This is an equation with the x at the power, so you have to write ${3}^{2 x}$ as an exponential (I assume x is a real number) since every real power function is in fact an exponential, hence the new equation : $\exp \left(2 x \ln \left(3\right)\right) = 81.$
You can now apply the natural logarithm at both sides of the equation (ln is a strictly growing function on R, which guanrantees you that the x you will find is unique) : $2 x \ln \left(3\right) = \ln \left(81\right)$.
Now you can divide on both sides by $2 \ln \left(3\right)$, and voilà!