Definitions for natural logarithm
nat·ural log·a·rithm

Princeton's WordNetRate this definition:0.0 / 0 votes

1. natural logarithm, Napierian logarithmnoun

   a logarithm to the base e

WiktionaryRate this definition:0.0 / 0 votes

1. natural logarithmnoun

   The logarithm in base e; either the function that given returns such that or the value of .

2. Etymology: From log naturalis, coined in 1668 by Nicholas Mercator in his book Logarithmo-technica.

WikipediaRate this definition:0.0 / 0 votes

1. Natural logarithm

   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 2.718281828459. 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 e2.0149... = 7.5. The natural logarithm of e itself, ln e, 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 (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural". The definition of the natural logarithm can then be extended to give logarithm values for negative numbers and for all non-zero complex numbers, although this leads to a multi-valued function: see Complex logarithm for more.

ChatGPTRate this definition:0.0 / 0 votes

1. natural logarithm

   The natural logarithm is a logarithm in the base e, where e is an irrational and constant number approximately equal to 2.718281828459. It is generally represented as ln(x) or log_e(x), where x is a positive real number. The natural logarithm turns multiplication into addition, raising e into the power of, and e-based exponential growth into linear growth. In calculus, physics, and complex analysis, natural logarithms are typically used as they are simpler and have nicer derivative properties.

WikidataRate this definition:0.0 / 0 votes

1. Natural logarithm

   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:

Matched Categories

1. • Logarithm

How to pronounce natural logarithm?

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How to say natural logarithm in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of natural logarithm in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of natural logarithm in Pythagorean Numerology is: 1

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=natural logarithm
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Natural_Logarithm
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Natural_Logarithm
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=natural logarithm