 Cologarithm
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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:

$\operatorname {colog} _{b}(x)=\log _{b}\left({\frac {1}{x}}\right)=\log _{b}(1)-\log _{b}(x)=-\log _{b}(x).$ The cologarithm in base b of a number is also equal to the logarithm of the same number having the reciprocal of b as the base:

$\operatorname {colog} _{b}(x)=\log _{\frac {1}{b}}(x).$ 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.

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