I’d just add to these explanations that it’s often helpful to look at some data after taking a logarithm. (Most of the time you take the log and multiply by 10). When you graph data that lives on a really big scale. This is clear from the fact that a log operation turns 100 into 2 and 1000 into 3, using the 10x method,, 100 becomes 20 and 1000 becomes 30. When you do it this way, the units of the answer are usually said to be in decibels which is written dB for short.

One thing commonly measured in dB is the “loudness” of sound as perceived by the ear. So if the sound goes up by 10 dB, the underlying data is going up by a factor of 10. 20 dB is a factor of 100.

The threshold of pain is up around 80 or 90 dB, and quiet is around 10 or so. The ear is very sensitive over a huge range!

Earthquakes are measured on the Richter scale, which doesn’t use the 10x, which means going up by 1, makes the earthquake 10x more powerful.

It’s also very common to use in engineering when comparing things like signal power and noise power, and many other comparative measures.

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