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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.\,}

Inchemistry, a decimal cologarithm is indicated by the letter p. For example, pK = – log10 K andpH = – log10 {H}

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