\begin{definition}[Definition:General Logarithm/Complex]
Let $z \in \C_{\ne 0}$ be a non-zero complex number.
Let $a \in \R_{>0}$ be a strictly positive real number such that $a \ne 1$.
The '''logarithm to the base $a$ of $z$''' is defined as:
:$\log_a z := \set {y \in \C: a^y = z}$
where $a^y = e^{y \ln a}$ as defined in Powers of Complex Numbers.
The act of performing the $\log_a$ function is colloquially known as '''taking logs'''.
\end{definition}