Logarithms

Logarithms are the true inverses of exponents, and follow the relation:

$y=a^{x} \Leftrightarrow x=\log_{a}{(x)}$

For the special value, Euler’s number, we have the natural logarithm:

$y=e^{x} \Leftrightarrow x = \ln{(y)}$

For positive values of $x$ and $y$, and when $a>0$ and $a\neq1$:

$\log_{a}{(xy)}=\log_{a}{x}+\log_{a}{y}$ $\log_{a}{\left(\frac{x}{y}\right)}=\log_{a}{x}-\log_{a}{y}$ $\log_{a}{(x)}^{n}=n\log_{a}{x}$