Conversion between Exponential and Logarithmic Form

For \(a>0,\ a\ne1\) and \(c>0\), exponential and logarithmic forms express the same relationship.

\(a^b=c\quad\Longleftrightarrow\quad b=\log_a c\)

\(a\) is the base and \(b\) is the index (exponent). The logarithm answers: “To what power must the base be raised?”

Take note

For \(x>0\), \(\log_{\mathrm e}x=\ln x\) and \(\log_{10}x=\lg x\).