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 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 R-log reduction is achieved, where
R = l o g 10 c b − l o g 10 c a = − l o g 10 ( c a c b ) {\displaystyle R=log_{10}{c_{\mathrm {b} }}-log_{10}{c_{\mathrm {a} }}=-log_{10}{\left({\frac {c_{\mathrm {a} }}{c_{\mathrm {b} }}}\right)}} .For the purpose of presentation, the value of R is rounded down to a desired precision, usually to a whole number.
ExampleLet the concentration of some contaminant be 580 ppm before and 0.725 ppm after treatment. Then
R = − l o g 10 ( 0.725 580 ) = − l o g 10 0.00125 ≈ 2.903 {\displaystyle R=-log_{10}{\left({\frac {0.725}{580}}\right)}=-log_{10}{0.00125}\approx 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 × c b − c a c b . {\displaystyle P=100~\times ~{\frac {c_{\mathrm {b} }-c_{\mathrm {a} }}{c_{\mathrm {b} }}}.} 2 ExampleLet, as in the earlier example, the concentration of some contaminant be 580 ppm before and 0.725 ppm after treatment. Then
P = 100 × 580 − 0.725 580 = 100 × 0.99875 = 99.875. {\displaystyle P~=~100~\times ~{\frac {580-0.725}{580}}~=~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.
| 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
References
"Final Report of an NWRI Independent Advisory Panel: Recommended DPR General Guidelines and Operational Requirements for New Mexico" (PDF). National Water Research Institute. January 22, 2016. Retrieved December 7, 2018. http://www.nwri-usa.org/pdfs/New-Mexico-DPR-Panel-General-Report(1).pdf ↩
"Log and Percent Reductions in Microbiology and Antimicrobial Testing". Microchem Laboratory. December 16, 2015. Retrieved December 7, 2018. https://microchemlab.com/information/log-and-percent-reductions-microbiology-and-antimicrobial-testing ↩