Another fun property of this is that you can use it across bases. For example, how many bits would I need to represent 34812923 in binary? log2(34812923) = 25.05 -> round up to 26 bits.

Thank you for posting this. The significance of this statement was lost on me until you pointed it out. Going by MathOverflow, it's slightly more complicated than that, but it's pretty close.

https://math.stackexchange.com/questions/1384917/relation-be...