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log reduction

{{Short description|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 {{math|n}}-log reduction means that the concentration of remaining contaminants is only {{math|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.{{cite web |title=Final Report of an NWRI Independent Advisory Panel: Recommended DPR General Guidelines and Operational Requirements for New Mexico |publisher=National Water Research Institute |url=http://www.nwri-usa.org/pdfs/New-Mexico-DPR-Panel-General-Report(1).pdf |date=January 22, 2016 |accessdate=December 7, 2018}}

Mathematical definition

Let {{math|cb}} and {{math|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 {{math|R}}-log reduction is achieved, where

: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 {{math|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=-log_{10}{\left(\frac{0.725}{580}\right)}=-log_{10}{0.00125}\approx 2.903

Rounded down, {{math|R}} is 2, so a 2-log reduction is achieved.

Conversely, an {{math|R}}-log reduction means that a reduction by a factor of {{math|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 {{math|cb}} and {{math|ca}} be as before, a reduction by {{math|P}} % is achieved, where

:P = 100~\times~\frac{c_\mathrm{b} - c_\mathrm{a}}{c_\mathrm{b}}.{{cite web |title=Log and Percent Reductions in Microbiology and Antimicrobial Testing |publisher=Microchem Laboratory |url=https://microchemlab.com/information/log-and-percent-reductions-microbiology-and-antimicrobial-testing |date=December 16, 2015 |accessdate=December 7, 2018}}

;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{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.

:

class="wikitable"

! 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 {{math|R}} is a whole number, an {{math|R}}-log reduction corresponds to a percentage reduction with {{math|R}} leading digits "9" in the percentage (provided that it is at least 10%).

See also

References

{{reflist}}

Category:Dimensionless numbers of chemistry

Category:Logarithmic scales of measurement

Category:Units of measurement

Category:Units of chemical measurement