every 3 powers of 2 the number of digits increases by 1. 50/3 = 16.67, so there are 16 digits.

First answer was close, but realize its going to be 50*log(3) ~ 15.05. Since this will be 1.xxx * 10^15, thats 16 digits. (1*10^1) is 2 digits

With these brain teasers, is it allowed to use scratch paper? Is there a favored approach between trying to work quickly and mentally as opposed to thoroughly and methodically? I can see the pro's and con's of both, and I'm just curious whether I should practice one way or another.

log2(2^50) / log2(10) = 50 / 3.3 ~= 15

2^50 / 10 = 16 * 2^46 *1.6