Logarithm of Logarithm in terms of Natural Logarithms

Theorem
Let $b, x \in \R_{>0}$ be (strictly) positive real numbers.

Then:
 * $\log_b \left({\log_b x}\right) = \dfrac {\ln \left({\ln x}\right) - \ln \left({\ln b}\right)} {\ln b}$

where $\ln x$ denotes the natural logarithm of $x$.