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Log reduction

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Measure of decontamination

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 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.

Example

Let 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 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 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} }}}.}
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 − 0.725 580   =   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

  1. "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.
  2. "Log and Percent Reductions in Microbiology and Antimicrobial Testing". Microchem Laboratory. December 16, 2015. Retrieved December 7, 2018.
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