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.

$\operatorname{colog}_b\ x = \log_b \left(\frac{1}{x} \right) = \log_b 1-\log_b x = -\log_b x \,$

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_a was later defined as –log₁₀ K_a.

References

• Meriam Webster definition of cologarithm
• "Cologarithm." From MathWorld--A Wolfram Web Resource.