Log reduction


Log reduction is a measure of how thoroughly a decontamination process reduces the concentration of a contaminant.
It is defined as the common logarithm of the ratio of the levels of contamination before and after the process, so an increment of 1 corresponds to a reduction in concentration by a factor of 10.
In general, an n-log reduction means that the concentration of remaining contaminants is only 10−n times that of the original. So for example, a 0-log reduction is no reduction at all, while a 1-log reduction corresponds to a reduction of 90 percent from the original concentration, and a 2-log reduction corresponds to a reduction of 99 percent from the original concentration.

Mathematical definition

Let b and a be the numerical values of the concentrations of a given contaminant, respectively before and after treatment, following a defined process.
It is irrelevant in what units these concentrations are given, provided that both use the same units.
Then an -log reduction is achieved, where
For the purpose of presentation, the value of is rounded down to a desired precision, usually to a whole number.
;Example:
Let the concentration of some contaminant be 580 ppm before and 0.725 ppm after treatment. Then
Rounded down, is 2, so a 2-log reduction is achieved.
Conversely, an -log reduction means that a reduction by a factor of 10 has been achieved.

Log reduction and percentage reduction

Reduction is often expressed as a percentage. The closer it is to 100%, the better.
Letting b and a be as before, a reduction by % is achieved, where
;Example:
Let, as in the earlier example, the concentration of some contaminant be 580 ppm before and 0.725 ppm after treatment. Then
So this is a 99% reduction, but not yet quite a 99.9% reduction.
The following table summarizes the most common cases.
In general, if is a whole number, an -log reduction corresponds to a percentage reduction with leading digits "9" in the percentage.