I can't do real division in my head, but if I wanted to maximise my logarithm-ability while minimizing my number of cards, I would go for logs base (probably 10) of primes, and 1/log(e) and 1/log(2).

But I'm not too fussed about minimizing cards, or about natural logs. Learning more primes might be helpful, but I can get them approximately. E.g. I don't have log_10(11) memorized, but I know it's between log_10(10) and log_10(2*6) which are 1 and 1.08, and it would be closer to the latter (my calculator says 1.041, which is slightly lower than I would have guessed, but if I put it in Anki I'd only go to 1.04 anyway).