What is a logarithmic scale? Why is it more useful for some things than a regular numerical scale?
In: Mathematics
Your standard scale will have evenly spaced lines at 1, 2, 3, 4, 5, 6, 7….
A log scale will have evenly spaced lines at 1, 10, 100, 1000, 10,000
Log scales are useful for looking at things that tend to grow exponentially [like say deaths in a pandemic](https://www.motherjones.com/wp-content/uploads/2020/05/blog_lse_linear_vs_log.jpg), they let you get details at both the lower end and the higher end.
If you look at the left plot on there, you really can’t get any details before it starts ramping up around March 22, everything left of that basically looks like its 0 because fitting both 10 and 40k on a graph with a linear scale really squishes data at the low end.
If you look at the right plot which is a semi-log (x axis is linear dates, y axis is a log scale) you can see that things start getting reported around March 4th and then proceeds to climb at roughly a straight line. If you plot something like 5^x on a semi-log plot like this you’ll get a straight line so when we look at exponential growth we expect to see a straight line.
Log plots are used whenever the difference between the smallest and largest number is several orders of magnitude. If you are plotting sound over time you’d work in dB which are a log scale because the difference between the loudest sound and the quietest sound you can hear is 10,000,000,000x difference in pressure
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