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Can you offer real-world examples of logarithm use?

An example of a real-world layman application of logarithms is understanding amplifier power ratings. For example a 30 watt amp is not one third as loud as 100 watt amp. It's actually 73% as the logarithm(base 100) of 30 = 0.73… 73%.

What are some other real-world layman examples of using logarithms?

Randy M Zeitman
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  • Amplification of anything in general. In signal processing or control engineering, things like noise suppression or sensitivity are commonly expressed using a logarithmic scale. Also things like the scale of an earthquake (Richter scale) is expressed as a logarithm. – Petrus1904 Jun 05 '21 at 17:13
  • @Petrus1904 Ah... earthquakes ... that's one, thank you. – Randy M Zeitman Jun 05 '21 at 17:19
  • Sound measurement but if you do a search on logarithms you can find more especially check out natural logs. – Solar Mike Jun 05 '21 at 17:30
  • real world? Logarithms and all measurements are human creations after there was some capacity available (due social organization) for something else than staying alive at least this day. Here's one: Lengths of numbers as well in 10-base and in binary system compared to the values of the numbers. –  Jun 05 '21 at 18:05
  • Oh Mike! Not the book! The Nautilus – StainlessSteelRat Jun 05 '21 at 18:46
  • For me, one of the most interesting uses in the pre-industrialized age for the use of Logarithms is in the precursors of (and the implementation of) the slide rule for multiplication and exponentiation. – Jim Clark Jun 06 '21 at 23:04

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Following are a few examples of logarithmic use. Some well know (like Richter and Decibel), some other more morbid (like pH, or spreading of diseases).

On each example, you could write a full answer, so I'll probably write a few words.

Radioactive decay time constant.

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Figure 1: Radioactive decay of element (source (Japanese ministry of the Environment)

Richter Scale: measuring earthquakes

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*Figure 2: Richter scale source: .maxwood.co *

Decibel Scale: tries to mimic the way the human ear interprets sound.

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Figure 3: Decibel scale source:commodious

light intensity

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Figure 4: Light intensity scale source:roguehealthandfitness

spreading rates of epidemics:

This and the following example (Viral Load) would probably not make this list if not for the global COVID-19 pandemic, which affects everyone (engineer or not).

During the spreading of the disease, in order to assess the spread rate, logarithmic plots are used because, the growth of the disease (if left unchecked) follows an exponential curve (See $R_t$ value greater than 1).

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Figure 5: Monitoring the exponential growth of Covid-19 cases in UK (linear left, exponential to the right). (source:roguehealthandfitness)

Viral load log scale:

The viral load is also actually (sometimes) measured in log scale. Basically, it reflects the fact that viruses effectively double in a pitri dish after a certain time constant, so you can tell how many you started with, by the time it took to fill the dish (a layman's explanation).

In particular, Covid-19 RT-PRC tests use the cycle threshold (CT) value. The CT value, which refers to the number of cycles in a RT-PCR test to amplify the viral RNA to reach a detectable level (the growth of the virus follows and exponential growth). I.e. the lower the number the higher the viral load.

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Figure 6: Viral Load . (source: Principles of Viral Load monitoring, ICAP Columbia University)

pH of solutions:

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Figure 7: pH scale explained in terms of presence of $OH^-$. (source:weebly)

NMech
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