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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.
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:<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]]

Latest revision as of 10:32, 4 December 2014

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