# Cologarithm

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:[1]

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 −log_{10} [H_{3}O^{+}]. Based on pH, the quantity p*K*_{a} was later defined as −log_{10} *K*_{a}.

## See also

## References

- 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.

## Further reading

- "Cologarithm".
*Merriam-Webster Dictionary*. Archived 16 February 2007 at the Wayback Machine. - "Cologarithm". Wolfram MathWorld.

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