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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 .

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