Definitions for natural logarithm
This page provides all possible meanings and translations of the word natural logarithm
Random House Webster's College Dictionary
a logarithm having e as a base.
Ref: Symbol: ln; Also called Napierian logarithm.; Compare common logarithm.
natural logarithm, Napierian logarithm(noun)
a logarithm to the base e
The logarithm in base e; either the function that given returns such that or the value of .
Origin: From log naturalis, coined in 1668 by Nicholas Mercator in his book Logarithmo-technica.
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828. The natural logarithm is generally written as ln x, loge x or sometimes, if the base of e is implicit, as simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x) or log(x). This is done in particular when the argument to the logarithm is not a single symbol, in order to prevent ambiguity. The natural logarithm of a number x is the power to which e would have to be raised to equal x. For example, ln is 2, because e²=7.389.... The natural log of e itself is 1 because e¹ = e, while the natural logarithm of 1 is 0, since e0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a. The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural." The definition can be extended to non-zero complex numbers, as explained below. The natural logarithm function, if considered as a real-valued function of a real variable, is the inverse function of the exponential function, leading to the identities:
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