Or you could, you know, think about how you define the function x -> log(x). Using the non-natural base is silly.
log(x) := (x -> 2^x)^(-1) ?
Seems a bit random to me. Why didn't you use pi?
actually I thought on using 5...
edit: And seriously, maybe because 2^x is the exponent that naturally appears in your field...
edit2: And what I actually want to hint on is: "How you define log" is not really a reason for one variant, as there are thousands of ways to define log, what's probably more important is "why you define log the way you do", but both "how" and "why" probably depends on context.