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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 2.718 281 828 459. [1] The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x.
The natural logarithm is asymptotically related to the harmonic numbers by the Stirling numbers [17] and the Gregory coefficients. [18] By representing H n {\displaystyle H_{n}} in terms of Stirling numbers of the first kind , the harmonic number difference is alternatively expressed as follows, for fixed k {\displaystyle k} :
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10.
List of logarithmic identities; Logarithm of a matrix; Logarithm table; ... Natural logarithm; Natural logarithm of 2; Natural logarithm plus 1; P. Pollard's kangaroo ...
This is a list of logarithm topics, by Wikipedia page. ... Natural logarithm. Natural logarithm of 2; Neper; Offset logarithmic integral; pH; Pollard's kangaroo ...
4.1 Natural logarithms. 4.2 Logarithms to arbitrary bases. 5 Trigonometric functions. ... This list is incomplete; you can help by adding missing items. (February 2011)
The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity.
is Euler's number, the base of natural logarithms, is the imaginary unit, which by definition satisfies =, and is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler.