natural logarithm

Also known as ln x, natural logarithm function, natural logarithmic function, natural log, natural lg, ln(x), Napierian logarithm, Naperian logarithm

logarithm to the base of the mathematical constant e

AI overview

The natural logarithm is a mathematical tool that answers the question "what power do I need to raise the number e to in order to get this result?" — it's essentially the reverse of exponential growth involving e, one of math's most important constants. It matters because exponential processes involving e appear everywhere in nature and science, from population growth to radioactive decay, making the natural logarithm essential for solving real-world problems.

AI-generated from the Wikipedia summary — may contain errors.

In the Vinony graph

Within Vinony's link graph, natural logarithm is referenced by 515 other articles, and connects out to Taylor series, common logarithm and logarithm.

It is catalogued under topics including Elementary special functions, E (mathematical constant) and Logarithms.

Its subject is documented across 64 Wikipedia language editions.

Wikidata facts

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Encyclopedic overview

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.

The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln 7.5 is 2.0149..., because e = 7.5. The natural logarithm of e itself, ln e, is 1, because e = e, while the natural logarithm of 1 is 0, since e = 1.

Excerpted from Wikipedia’s “natural logarithm” article, available under the CC BY-SA 4.0 licence.