Difference between revisions of "Natural logarithm"

Revision as of 14:34, 18 August 2006

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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-The '''natural logarithm''', denoted <math>\ln</math>, is the [[logarithm]] with [[base]] [[e]].  Thus <math> \ln(x) = \log_e(x).</math>
+The '''natural logarithm''' is the [[logarithm]] with [[base]] [[e]].  It is usually denoted <math>\ln</math>, an abbreviation of the French ''logarithme normal'', so that <math> \ln(x) = \log_e(x).</math>  However, in higher mathematics such as [[complex analysis]], the base 10 logarithm is typically disposed with entirely, the symbol <math>\log</math> is taken to mean the logarithm base e and the symbol <math>\ln</math> is not used at all.  (This is an example of conflicting [[mathematical convention]]s.)
 == Calculus definition ==
-In calculus, the natural logarithm is defined such that <math>\ln(x) = \int_1^x \frac 1x \ dx</math>.
+In calculus, the natural logarithm is defined by <math>\ln(x) = \int_1^x \frac 1x \ dx</math>.
 [[Category:Definition]]
+----

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Difference between revisions of "Natural logarithm"

Revision as of 14:34, 18 August 2006

Calculus definition