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Natural logarithm

From AoPSWiki

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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