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#REDIRECT ]
In ], the base-''b'' '''cologarithm''',<ref name="Hall_1909"/> sometimes shortened to '''colog''',<ref name="Hall_1909"/> of a number is the base-''b'' ] of the ] of the number. It is equal to the ''negative'' base-''b'' logarithm of the number.


⚫ ]
:{{nowrap|<math> \operatorname{colog}_b (x) = \log_b \left(\frac{1}{x} \right) = \log_b (1) - \log_b (x) = -\log_b (x)</math><ref name="Hall_1909"/>}}


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The cologarithm in base b of a number is also equal to the logarithm of the same number having the reciprocal of b as the base:
{{R from related word}}

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:{{nowrap|<math> \operatorname{colog}_b (x) = \log_{\frac{1}{b}} \left(x \right)</math>}}
{{R with history}}

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In ], a decimal cologarithm is indicated by the letter p. This usage originated with the quantity ], defined as –log<sub>10</sub> . Based on pH, the quantity ] was later defined as –log<sub>10</sub> ''K''<sub>a</sub>.

== See also ==
* ]

== References ==
{{reflist|refs=
<ref name="Hall_1909">{{cite book |title=Trigonometry |volume=Part I: Plane Trigonometry |author-first1=Arthur Graham |author-last1=Hall |author-first2=Fred Goodrich |author-last2=Frink |date=January 1909 |location=Ann Arbor, Michigan, USA |chapter=Chapter IV. Logarithms Cologarithms |publisher=] / Norwood Press / J. S. Cushing Co. - Berwick & Smith Co., Norwood, Massachusetts, USA |publication-place=New York, USA |page=36 |url=https://archive.org/stream/planetrigonometr00hallrich#page/n51/mode/1up |access-date=2017-08-12 }}</ref>
}} }}

==Further reading==
*
*

{{algebra-stub}}

⚫ ]

Latest revision as of 20:38, 9 February 2023

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