Log reduction

 ( Dimensionless Numbers Of Chemistry ) 

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 -log reduction means that the concentration of remaining contaminants is only 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.

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Mathematical definition Let and 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 -log reduction is achieved, where

$R=\backslash log\_\{10\}\{c\_\backslash mathrm\{b\}\}-\backslash log\_\{10\}\{c\_\backslash mathrm\{a\}\}=-\backslash log\_\{10\}\{\backslash left(\backslash frac\{c\_\backslash mathrm\{a\}\}\{c\_\backslash mathrm\{b\}\}\backslash right)\}$.

For the purpose of presentation, the value of 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

$R=-\backslash log\_\{10\}\{\backslash left(\backslash frac\{0.725\}\{580\}\backslash right)\}=-\backslash log\_\{10\}\{0.00125\}\backslash approx\; 2.903$

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

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

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

$P\; =\; 100~\backslash times~\backslash frac\{c\_\backslash mathrm\{b\}\; -\; c\_\backslash mathrm\{a\}\}\{c\_\backslash mathrm\{b\}\}.$

Example

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

$P~=~100~\backslash times~\backslash frac\{580\; -\; 0.725\}\{580\}~=~100~\backslash times~0.99875~=~99.875.$

So this is (better than) a 99% reduction, but not yet quite a 99.9% reduction.

The following table summarizes the most common cases.

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

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See also

• Decimal reduction time

Categories: Dimensionless Numbers Of Chemistry, Logarithmic Scales Of Measurement, Units Of Measurement, Units Of Chemical Measurement

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