How exactly does a logarithmic scale work?

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I’m unable to detach my mind from the linear scale imbedded in my head, how to make sense of a logarithmic increase?

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Anonymous 0 Comments

In addition to the other replies here about putting a log scale on the y-axis, there are also times when it makes sense to put the log scale on the x-axis as well (known as a log-log scale). These can be useful in cases where, for example, you have a lot of data on the past, but lots of the interesting changes are taking part in the last (most recent) data.

Here are some interesting charts to compare, all showing the exact same data: world population from 10000BC to 2000AD.

[Linear scale:](https://upload.wikimedia.org/wikipedia/commons/b/b7/Population_curve.svg) looks essentially flat for thousands of years, some stuff starts happening around 1AD but it still looks fairly insignificant, and then there is a huge spike right at the end, but you can’t really tell what year the spike really started.

[Log scale:](https://upload.wikimedia.org/wikipedia/commons/f/f2/World_population_growth_%28lin-log_scale%29.png) you can see a lot more detail of the population fluctuations thousands of years ago, that all looked like “0” on the linear scale. There is still a massive spike right at the end of the 20th century, but you still can’t see down to what’s happening decade-to-decade.

[Log-log scale](https://upload.wikimedia.org/wikipedia/commons/8/84/World_population_growth_%28log-log_scale%29.png): now the thousands of years of data from long ago are compressed (but you can still see the fluctuations clearly), and the data is more zoomed-in as you get more recent- since more recent trends are probably what we’re more interested in.

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