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