Logarithm of Power/General Logarithm

Theorem
Let $x \in \R$ be a strictly positive real number.

Let $a \in \R$ be a real number such that $a > 1$.

Let $r \in \R$ be any real number.

Let $\log_a x$ be the logarithm to the base $a$ of $x$.

Then:
 * $\map {\log_a} {x^r} = r \log_a x$

Proof
Let $y = r \log_a x$.

Then:

The result follows by taking logs base $a$ of both sides.