Cologarithm

What is a cologarithm?

A cologarithm is the negative of a logarithm. In practice, it is obtained by changing the sign of the logarithmic value.

$$ \text{colog}_b \ x = - \log_b x $$

This means that every logarithm has a corresponding cologarithm with the opposite sign.

Example

Consider the logarithm of 8 in base 2.

$$ \log_2 8 $$

The corresponding cologarithm is

$$ \text{colog}_2 \ 8 = - \log_2 8 $$

Since

$$ \log_2 8 = 3 $$

the cologarithm is

$$ \text{colog}_2 \ 8 = -3 $$

In other words, a cologarithm represents the same logarithmic value with the sign reversed.

The same idea applies to logarithms in any base.