Wednesday, November 29, 2023

# What is a semi-log plot and how can you use it for Covid data?

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Just to be clear, 106 means 10 x 10 x 10 x 10 x 10 x 10. But what if I want to do the inverse of 10 raised to a certain power? It is much easier to write large numbers by raising them to a certain power – this is exactly what we do with numbers in scientific notation. Finding the power of 10 that a number is high is exactly what a logarithm does. If I take the log of 1,000,000, that gives the result of 6. Oh, here’s an important note. If we are talking about 10 raised to a certain power, that means we are using a logarithmic base of 10. The two most common bases are 10 (because we write numbers in base 10) or e, the natural number where e is about 2.718 (this is irrational). Here is a more detailed explanation of th.

But wait! You can also take the logarithm for numbers that are not whole powers of 10. Let’s just take a number – I’m going with 1,234. If I take the logarithm of that number, I get:

This means that if you increase 10 to the power of 3.09132, you get 1234. But why? Why would you do that? OK, back to our terrible Covid data. Suppose instead of plotting the number of confirmed infections, I plot the log (base 10) of the number of infections. I can then plot the log of the number versus the number of days. Here is what it looks like.