Logarithmic functions have the form \(f(x)=\log_b x\), where \(b\) is the base.
They are the inverse of Exponential functions such that \(\log_b x = y \iff x = b^y\).
\[ \log_b m \times n = \log_b m + \log_b n \] \[ \log_b \frac m n = \log_b m - \log_b n \] \[ \log_b m^n = n \log_b m \] \[ \log_b 1 = 0 \] \[ \log_b b = 1 \] \[ \log_{b}a = \frac{\log_{10}a}{\log_{10}b} = \frac{\ln{a}}{\ln{b}}\]