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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 (origonally the Greek letter ρ){{fact}}.<br />For example, ] = – log<sub>10</sub> ''K'' and] = – log<sub>10</sub> . In], a decimal cologarithm is indicated by the letter p (origonally 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 01:03, 10 June 2009

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.\,}

Inchemistry, a decimal cologarithm is indicated by the letter p (origonally the Greek letter ρ).
For example, pK = – log10 K andpH = – log10 .

References

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