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In mathematics, the base-b cologarithm,[1] sometimes shortened to colog,[1] 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.


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:

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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  1. ^ a b c Hall, Arthur Graham; Frink, Fred Goodrich (January 1909). "Chapter IV. Logarithms [28] Cologarithms". Written at Ann Arbor, Michigan, USA. Trigonometry. Part I: Plane Trigonometry. New York, USA: Henry Holt and Company / Norwood Press / J. S. Cushing Co. - Berwick & Smith Co., Norwood, Massachusetts, USA. p. 36. Retrieved 2017-08-12.

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