{{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<sup>−''n''</sup>}} 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.<ref>{{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}}</ref>
==Mathematical definition== Let {{math|''c''<sub>b</sub>}} and {{math|''c''<sub>a</sub>}} 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
:<math>R=\log_{10}{c_\mathrm{b}}-\log_{10}{c_\mathrm{a}}=-\log_{10}{\left(\frac{c_\mathrm{a}}{c_\mathrm{b}}\right)}</math>.
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
:<math>R=-\log_{10}{\left(\frac{0.725}{580}\right)}=-\log_{10}{0.00125}\approx 2.903</math>
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|10<sup>''R''</sup>}} 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|''c''<sub>b</sub>}} and {{math|''c''<sub>a</sub>}} be as before, a reduction by {{math|''P''}} % is achieved, where :<math>P = 100~\times~\frac{c_\mathrm{b} - c_\mathrm{a}}{c_\mathrm{b}}.</math><ref>{{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}}</ref> ;Example: Let, as in the earlier example, the concentration of some contaminant be 580 ppm before and 0.725 ppm after treatment. Then :<math>P~=~100~\times~\frac{580 - 0.725}{580}~=~100~\times~0.99875~=~99.875.</math> 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== *Decimal reduction time
==References== {{reflist}}
Category:Dimensionless numbers of chemistry Category:Logarithmic scales of measurement Category:Units of measurement Category:Units of chemical measurement