Thursday, October 2, 2008

How many digits does 2 "raise to" 1000 have?

We have to find decimal (base 10) digits. So convert to base 10.

21000 = 10(log 2)1000

Now 101, 102, and 103 has 2, 3, and 4 digits respectively.

So 21000 should have approximately (log 2)1000 + 1 digits.

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