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 -log reduction means that the concentration of remaining contaminants is only 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 and 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

:$R=log_-log_=-log_$.

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

:$R=-log_=-log_\approx 2.903$

Rounded down, is 2, so a 2-log reduction is achieved.

Conversely, an -log reduction means that a reduction by a factor of has been achieved.

Log reduction and percentage reduction

Reduction is often expressed as a percentage. The closer it is to 100%, the better.
Letting and be as before, a reduction by  % is achieved, where
:$P = 100~\times~\frac.$
;Example:
Let, as in the earlier example, the concentration of some contaminant be 580 ppm before and 0.725 ppm after treatment. Then
:$P~=~100~\times~\frac~=~100~\times~0.99875~=~99.875.$
So this is (better than) 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 (provided that it is at least 10%).

See also

* Decimal reduction time

References

{{reflist

Dimensionless numbers of chemistry
Logarithmic scales of measurement
Units of measurement
Units of chemical measurement