Introduction: Sometimes it can be useful to change the base of a logarithmic function.
Theorem: $^a\!\log x={\displaystyle \frac{^b\!\log x}{^b\!\log a}}$
Example: $^4\!\log 9= \dfrac{^2\!\log 9}{^2\!\log 4}=\dfrac{^2\!\log 3^2}{^2\!\log 2^2}=\dfrac{2\cdot^2\!\log 3}{2\cdot^2\!\log 2}=^2\!\log 3$.
Theorem: $^a\!\log x={\displaystyle \frac{^b\!\log x}{^b\!\log a}}$
Example: $^4\!\log 9= \dfrac{^2\!\log 9}{^2\!\log 4}=\dfrac{^2\!\log 3^2}{^2\!\log 2^2}=\dfrac{2\cdot^2\!\log 3}{2\cdot^2\!\log 2}=^2\!\log 3$.