Log reduction

Key takeaways

Log reduction belongs to chemistry; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Log reduction to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Log reduction from memory before moving on to harder problems.

Reference excerpt

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−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.

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 = log 10 ⁡ c b − log 10 ⁡ c a = − log 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 = − log 10 ⁡ ( 0.725 580 ) = − log 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 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 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.

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%).

Worked examples

Example 1 — a first encounter with Log reduction

Start with the simplest possible case. Write down what Log reduction claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Log reduction before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Log reduction ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Log reduction

In research: Log reduction appears in chemistry research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Log reduction in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Log reduction is common in secondary-school and first-year university syllabi. It links to neighbouring topics Dimensionless numbers of chemistry, Logarithmic scales of measurement, Units of chemical measurement, so understanding it makes those chapters shorter.
In everyday life: Look for Log reduction outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Log reduction in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Log reduction means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Log reduction out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Log reduction in simple terms?

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 fa…

Why does Log reduction matter?

Because it connects several chemistry ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Log reduction?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Log reduction.