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.

 \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 pK was later defined as –log10 K.

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