Earthquake magnitude is a logarithmic measure of earthquake size.

Stated more simply the logarithmic measure of variety represents the minimum number of choices (by binary chop) needed to resolve uncertainty.

Specifically, entropy is a logarithmic measure of the number of states with significant probability of being occupied:

A logarithmic measure of the brightness of an astronomical object:

SPL is a logarithmic measure of the rms sound pressure of a sound relative to a reference value.

The difference between two sound powers can be express in decibels (logarithmic measure) using this equation:

It is a logarithmic measure of the ratio of two sound energy densities.

Deviating from these units means that the logarithmic measure will change by an additive constant.

Ralph Hartley suggested the use of a logarithmic measure of information in 1928.

In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution.