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# Logarithmic functions

Logarithmic functions have the form \(f(x)=\log_b x\), where \(b\) is the base.

They are the inverse of Exponential functions such that \(\log_b x = y \iff x = b^y\).

## Identities

\[
\log_b m \times n = \log_b m + \log_b n
\]
\[
\log_b \frac m n = \log_b m - \log_b n
\]
\[
\log_b m^n = n \log_b m
\]
\[
\log_b 1 = 0
\]
\[
\log_b b = 1
\]