Logarithms and Exponentials

An exponential is $a^x=n$, a logarithm is $\log_{a}n=x$ where $a$ is the base, $x$ is the power, and $n$ is the result. Exponentials and logarithms are inverses of eachother. The constant $e$ is a special case, in which its inverse is the natural log, or $\ln n=x$, which is equivalent to $log_{e}n=x$.

This property applies to equations that look like $a^x = a^y$. If $x = y$, then you can drop the exponent. The same works for logs (i.e. $\ln x = \ln y$ → $x = y$).