Natural logarithm

Revision as of 15:34, 18 August 2006 by JBL (talk | contribs)

The natural logarithm is the logarithm with base e. It is usually denoted $\ln$, an abbreviation of the French logarithme normal, so that $\ln(x) = \log_e(x).$ However, in higher mathematics such as complex analysis, the base 10 logarithm is typically disposed with entirely, the symbol $\log$ is taken to mean the logarithm base e and the symbol $\ln$ is not used at all. (This is an example of conflicting mathematical conventions.)

Calculus definition

In calculus, the natural logarithm is defined by $\ln(x) = \int_1^x \frac 1x \ dx$.

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