Cologarithm


Cologarithm

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.

 \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)[citation needed].
For example, pK = – log10 K and pH = – log10 [H3O+].

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