Iterated Logarithm. Just don’t get it.

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Iterated Logarithm. Just don’t get it.

In: Mathematics

You can think about division like this: to calculate a/b, subtract b from a again and again until you reach 0. The number of times you subtracted is a/b.

Similarly, you can think of log the same way: to calculate logb(a), divide a by b again and again until you reach 1. The number of times you divided is logb(a).

So iterated logarithm is the next level: to calculate log*b(a), take logb of a again and again until you reach 1, and count the number of times.

A logarithm has a base (usually 10 or e).

Log of something is the power you’d have to raise the base to get that number. My post will be about log base 10 for simplicity.

10^4 =10000

Log(10000) = 4

Great, now what is the iterative logarithm? Basically you keep taking the log until you get an answer that’s less than or equal to one, the number of times you do this is the iterative logarithm.

1. Log(10^100) = 100
2. Log(100) = 10
3. Log(10) = 1

Iterative log = 3

Another example:

1. Log(1234567890) = 9.091514977
2. Log(9.091514977) = 0.958636258

Iterative log = 2