“Log reduction”的意思、由来-开放百科全书

词条

Log reduction

释义

Mathematical definition
Log reduction and percentage reduction
See also
References

The log reduction achieved by a decontamination process is a measure of the reduction in the concentration of a contaminant. The name reflects that the measure is expressed on a logarithmic scale, using base 10. An increase by 1 corresponds to a reduction in the concentration of the contaminant by a factor of 10. A 0-log reduction means that there is no reduction. A 1-log reduction would correspond to a reduction of 90 percent from the original concentration. A 2-log reduction corresponds to a reduction of 99 percent from the original concentration.^[1]

Mathematically, the log reduction is the base-10 logarithm of the ratio between the concentrations before and after treatment. Some other measures using a logarithmic scale to express a ratio are the decibel, the astronomical magnitude and the pH scale.

Mathematical definition

Let {{mvar|c}}_b and {{mvar|c}}_a 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 {{mvar|R}}-log reduction is achieved, where

{{mvar|R}} = log₁₀ {{mvar|c}}_b − log₁₀ {{mvar|c}}_a = − log₁₀ ({{mvar|c}}_a / {{mvar|c}}_b).

For the purpose of presentation, the value of {{mvar|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

{{mvar|R}} = − log₁₀ (0.725/580) = − log₁₀ 0.00125 = 2.903...

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

Conversely, an {{mvar|R}}-log reduction means that a reduction by a factor of 10^{{mvar|R}} has been achieved.

Log reduction and percentage reduction

Reduction is often expressed as a percentage. The closer it is to 100%, the better.

Letting {{mvar|c}}_b and {{mvar|c}}_a be as before, a reduction by {{mvar|P}}% is achieved, where

^[2]

Example

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

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

References

1. ^{{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}}
2. ^{{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}}

4 : Dimensionless numbers|Logarithmic scales of measurement|Units of measurement|Units of chemical measurement

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

Mathematical definition

Log reduction and percentage reduction

See also

References