what exactly *is* a logarithm and what does it do?

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I mean, I’ve used them in algebra many times but I never really understood what it does. Kinda like in biostatistics how I could do the math, but how it worked was beyond me entirely.

So yeah: like what’s this sorcery and what does it do/why do we use it?

In: Mathematics

26 Answers

Anonymous 0 Comments

Logarithm is the inverse of exponentiation, for example:

10^2 = 100, log(100) = 2.

Note, for the logarithm you have to specify the base, for example:

2^5 = 32, log2(32) = 5, but log10(32) ~1.505…

Logarithms are sometimes used for plotting data that grows exponentially. For example if you were to plot inflation vs time, you’d find the growth so rapid you couldnt adequately visualize data from 50 to 100 years ago. Plotting the logarithm of inflation vs time, however, clearly shows a long term trend.

The mathematics goes way beyond these examples, so would only use them as a starting point. For example, you can describe rotations using logarithms, but the math can be advanced.

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