TITLE: Is there a way to find the log of very large numbers?
QUESTION [30 upvotes]: I should like to evaluate $\log_2{256!}$ or other large numbers to find 'bits' of information. For example, I'd need three bits of information to represent the seven days of the week since $\lceil \log_2{7}\rceil = 3$, but my calculator returns an error for large numbers.

REPLY [4 votes]: If the number is not a factorial but rather any large number then a cutest way would be to consider the fundamental theorem of number theory. 
says for any integer $n$ we have  $$n =\prod p_i^{a_i}$$ where p_i's are prime numbers. then by the law of log you get $$\log n= \sum a_i\log p_i.  $$