natural logarithm

American  

noun

Mathematics.

1. a logarithm having e as a base. ln

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natural logarithm British  

noun

1. Also called: Napierian logarithm.  a logarithm to the base e. Usually written log e or ln Compare e common logarithm

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natural logarithm Scientific  

1. A logarithm using base e. Natural logarithms are common in mathematics, especially in cases involving complex numbers. They are also called Napierian logarithms, after their inventor, English mathematician John Napier (1550–1617).

2. See more at e Compare common logarithm

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Etymology

Origin of natural logarithm

First recorded in 1810–20

Example Sentences

In that case we often take the common logarithm or natural logarithm of both sides once the exponential is isolated.

From Textbooks • May 6, 2020

Note that if we use the absolute value function and create a new function ln |x|, we can extend the domain of the natural logarithm to include x < 0.

From Textbooks • Mar. 30, 2016

Note that the natural logarithm is one-to-one and therefore has an inverse function.

From Textbooks • Mar. 30, 2016

Note that general logarithm functions can be written in terms of the natural logarithm.

From Textbooks • Mar. 30, 2016

Since L’Hôpital’s rule applies to quotients, we use the natural logarithm function and its properties to reduce a problem evaluating a limit involving exponents to a related problem involving a limit of a quotient.

From Textbooks • Mar. 30, 2016