Exponential and Logarithmic Functions - Conversion between Exponential and Logarithm Form

All real logarithms below have positive arguments and a positive base different from 1. In the power law, the argument before raising it to a power is positive.

Conversion between Exponential and Logarithmic Form

\({{a}^{b}}=c\underset{{}}{\longleftrightarrow}b={{\log }_{a}}c\)

\(a\) : base \(\quad\) \(b\) : index

Important Notes:

• \(a>0,c>0\)

• \({{\log }_{\mathrm{e}}}x=\ln x\) and \({{\log }_{10}}x=\lg x\)