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.[1]

## Contents

* 1 Mathematical definition
* 2 Log reduction and percentage reduction
* 3 See also
* 4 References

## Mathematical definition

Let cb and ca 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 and R-log reduction is achieved, where

R=log10cb−log10ca=−log10(cacb).

For the purpose of presentation, the value of R 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=−log10(0.725580)=−log100.00125≈2.903

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

Conversely, an R-log reduction means that a reduction by a factor of 10R has been achieved.

## Log reduction and percentage reduction

Reduction is often expressed as a percentage. The closer it is to 100%, the better. Letting cb and ca be as before, a reduction by P % is achieved, where

P=100×cb−cacb.[2]
Example

Let, as in the earlier example, the concentration of some contaminant be 580 ppm before and 0.725 ppm after treatment. Then

P=100×580−0.725580=100×0.99875=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.

Log reduction  | Percentage

|

1-log reduction  | 90%
2-log reduction  | 99%
3-log reduction  | 99.9%
4-log reduction  | 99.99%
5-log reduction  | 99.999%

In general, if R is a whole number, an R-log reduction corresponds to a percentage reduction with R leading digits "9" in the percentage (provided that it is at least 10%).

## See also

* Decimal reduction time

## References

1. ↑ "Final Report of an NWRI Independent Advisory Panel: Recommended DPR General Guidelines and Operational Requirements for New Mexico". National Water Research Institute. January 22, 2016. http://www.nwri-usa.org/pdfs/New-Mexico-DPR-Panel-General-Report(1).pdf. Retrieved December 7, 2018.
2. ↑ "Log and Percent Reductions in Microbiology and Antimicrobial Testing". Microchem Laboratory. December 16, 2015. https://microchemlab.com/information/log-and-percent-reductions-microbiology-and-antimicrobial-testing. Retrieved December 7, 2018.

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