Logarithms

If $y = a^x$ then $\log_a y = x$

Another way to think of it is, what value taken to the power of a is equal to y?

Common bases

When the base isn't specified, it usually means $log_{10}$ eg: $\log b = \log_{10} b$

The "natural log" refers to the log $e$ $\ln b = \log_{e} b$

Change of base formula

$\log_a b = \frac{\log_x b}{\log_x a}$ where $x$ is an arbiraty we're trying to change to.

Source: Evalulating logarithms: change of base rule