For a>0, a 1 and c>0, exponential and logarithmic forms express the same relationship. ab=c 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_ ex=ln x and log_10x=lg x.

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?”

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

Exponential and Logarithmic Functions

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Conversion between Exponential and Logarithmic Form

Conversion between Exponential and Logarithmic Form