# Cologarithm

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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.

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

In chemistry, a decimal cologarithm is indicated by the letter p. This usage originated with the quantity pH, defined as –log10 [H3O+]. Based on pH, the quantity pKa was later defined as –log10 Ka.