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In ], the base-''b'' '''cologarithm''' of a number, sometimes shortened to '''colog''', is the base-''b'' ] of the ] of the number. This means that In ], the base-''b'' '''cologarithm''', sometimes shortened to '''colog''', of a number is the base-''b'' ] of the ] of the number. It is equal to the ''negative'' base-''b'' logarithm of the number.


:<math> \operatorname{colog}_b\ x = \log_b \left(\frac{1}{x} \right) = -\log_b x = \log_{1/b} x.\, </math> :<math> \operatorname{colog}_b\ x = \log_b \left(\frac{1}{x} \right) = \log_b 1-\log_b x = -\log_b x = \log_{1/b} x.\, </math>


== References == == References ==

Revision as of 18:37, 23 March 2008

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.

colog b ⁡   x = log b ⁡ ( 1 x ) = log b ⁡ 1 − log b ⁡ x = − log b ⁡ x = log 1 / b ⁡ x . {\displaystyle \operatorname {colog} _{b}\ x=\log _{b}\left({\frac {1}{x}}\right)=\log _{b}1-\log _{b}x=-\log _{b}x=\log _{1/b}x.\,}

References

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