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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> :<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], a decimal cologarithm is indicated by the letter p (originally the Greek letter ρ){{Fact|date=June 2009}}.<br />For example, ] = – log<sub>10</sub> ''K'' and] = – log<sub>10</sub> . In ], a decimal cologarithm is indicated by the letter p (originally the Greek letter ρ){{Fact|date=June 2009}}.<br />For example, ] = – log<sub>10</sub> ''K'' and ] = – log<sub>10</sub> .


== References == == References ==

Revision as of 17:53, 6 April 2010

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.

colog b   x = log b ( 1 x ) = log b 1 log b x = log b x = log 1 / b x . {\displaystyle \operatorname {colog} _{b}\ x=\log _{b}\left({\frac {1}{x}}\right)=\log _{b}1-\log _{b}x=-\log _{b}x=\log _{1/b}x.\,}

In chemistry, a decimal cologarithm is indicated by the letter p (originally the Greek letter ρ).
For example, pK = – log10 K and pH = – log10 .

References

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