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In [[mathematics]], the base-''b'' '''cologarithm''', sometimes shortened to '''colog''', of a number is the base-''b'' [[logarithm]] of the [[multiplicative inverse|reciprocal]] of the number. It is equal to the ''negative'' base-''b'' logarithm of the number. | |||
:<math> \operatorname{colog}_b\ x = \log_b \left(\frac{1}{x} \right) = \log_b 1-\log_b x = -\log_b x = \log_{1/b} x.\, </math> | |||
In [[chemistry]], a decimal cologarithm is indicated by the letter p (originally the Greek letter ρ){{Fact|date=June 2009}}.<br />For example, [[acid dissociation constant|p''K'']] = – log<sub>10</sub> ''K'' and [[pH]] = – log<sub>10</sub> [H<sub>3</sub>O<sup>+</sup>]. | |||
== References == | |||
*[http://www.merriamwebster.com/dictionary/cologarithm Meriam Webster definition of cologarithm] | |||
*[http://mathworld.wolfram.com/Cologarithm.html "Cologarithm." From MathWorld--A Wolfram Web Resource.] | |||
{{algebra-stub}} | |||
[[Category:Special functions]] | |||
Revision as of 23:47, 25 November 2013
In mathematics, the base-b cologarithm, sometimes shortened to colog, of a number is the base-b logarithm of the reciprocal of the number. It is equal to the negative base-b logarithm of the number.
In chemistry, a decimal cologarithm is indicated by the letter p (originally the Greek letter ρ)Template:Fact.
For example, pK = – log10 K and pH = – log10 [H3O+].