# 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

Logarithms feel a bit like asking “how many digits (after the first) does this number have?” or “what order of magntidue is this number?”, although with some more nuance.

Consider log to the base 10.

So log1=0

log10=1

log100=2

log1000=3

etc, so for any power of 10, log(base10) gives us that power.

The log function also gives us an answer in-between these values, like log50 ~= about 1.7.

Often people will use base-2 to talk about computing. This will sometimes imply some logarithms, telling us how many *binary* digits (1s and 0s) the computer is using.

For instance “This is a 64 bit processor.” means “The log (to base 2) of the number of memory addresses this processor can imagine, is 64.” i.e. “It can imagine 2^64 memory addresses.”

Mathematicians often use log to base “e”, where e refers to a specifical useful constant, similar to how pi is useful, in how it appears in many interesting formula.