Is there a way to find the log of very large numbers? 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.
By the laws of logarithms

$$ \log_2(256!) = \sum_{i=1}^{256} \log_2(i)$$

This is easily evaluated (albeit not on all calculators).

In Python:

&gt;&gt;&gt; sum(math.log2(i) for i in range(1,257))
1683.9962872242136
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