Compacting a number scale using a logarithmic function

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I have a range of values that range from 31 to 2147. I'd like to be able to represent these numbers on a graph containing 120 points. Smaller numbers are more "important" and I'd like more visual discrimination between 31 and 35 for instance than between 2140 and 2145.

I can linearly interpolate the numbers and make each interval 17.64 (so lumping all numbers between 31 and 47 into one point), but that doesn't achieve my goal. Unfortunately, I don't know how to do this logarithmic ally and I don't have enough math to understand any of the articles I've found.

I'm hoping someone can help me with a transformation formula to apply to my numbers so I can achieve the desired result.

So I guess I'm asking if there is a formula for logarithmic interpolation?