Apparently the bit pattern of a float interpreted as an int is sorta-kinda it's own logarithm, which is why the famous fast inverse square root from quake 3 works: log(x^-½) = -½log(x) =~ -log(x) >> 1. This video is approachable and explains it pretty well: https://www.youtube.com/watch?v=p8u_k2LIZyo
