Logarithm of Power/Natural 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 $\ln x$ be the natural logarithm of $x$.

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