Algorithm for logarithmically converting a number to a percentage

logarithm, math

Solution

try `1 / (1 + e^(1-x))`

it's the logistic function shifted by 1 unit

If you want it to approach faster, you can change e to something higher

Edit:

to have f(0) = 0 you could use `1 - 2^(-x)`

Problem

I am looking for a way to convert any number to a percentage in the following way: 1.00 is 50% numbers below 1.00 approach 0% logarithmically numbers above 1.00 approach 100% logarithmically. x > 0. So y needs to approach 0 as x becomes infinitely small on the positive side. I'm sure this is simple to do, but I can't recall how to do it.

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