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In mathematics, the common logarithm (aka "standard logarithm") is the logarithm with base 10. [1] It is also known as the decadic logarithm , the decimal logarithm and the Briggsian logarithm . The name "Briggsian logarithm" is in honor of the British mathematician Henry Briggs who conceived of and developed the values for the "common logarithm".
In chemistry the negative of the decimal logarithm, the decimal cologarithm, is indicated by the letter p. [63] For instance, pH is the decimal cologarithm of the activity of hydronium ions (the form hydrogen ions H + take in water). [64] The activity of hydronium ions in neutral water is 10 −7 mol·L −1, hence a pH of 7. Vinegar typically ...
The area of the blue region converges to Euler's constant. Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma (γ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log:
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.
All instances of log(x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln(x) or log e (x). In number theory , an arithmetic , arithmetical , or number-theoretic function [ 1 ] [ 2 ] is generally any function whose domain is the set of positive integers and whose range is a subset of the complex ...
For example, class 5 is defined to include numbers between 10 10 10 10 6 and 10 10 10 10 10 6, which are numbers where X becomes humanly indistinguishable from X 2 [14] (taking iterated logarithms of such X yields indistinguishibility firstly between log(X) and 2log(X), secondly between log(log(X)) and 1+log(log(X)), and finally an extremely ...
Napier's "logarithm" is related to the natural logarithm by the relation ()and to the common logarithm by ().Note that and (). Napierian logarithms are essentially natural logarithms with decimal points shifted 7 places rightward and with sign reversed.
A page from Henry Briggs' 1617 Logarithmorum Chilias Prima showing the base-10 (common) logarithm of the integers 0 to 67 to fourteen decimal places. Part of a 20th-century table of common logarithms in the reference book Abramowitz and Stegun. A page from a table of logarithms of trigonometric functions from the 2002 American Practical Navigator.
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