Question 254315: How many digits does 2^15 * 5^8 have when expanded? Found 2 solutions by drk, richwmiller:Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! The number of digits in 2^15 = 32768 = 5.
The number of digits in 5^8 = 390625 = 6.
multiplied together, we get 11 digits.
There can be a shortcut but it involves formulas.
The number of digits of a^b can be approximated by
(i) N = b*log(a)
applying the original information, we get
(ii) 15log(2) ~ 4.515 take the digit and add 1 to get 5.
(iii) 8log(5) ~ 5.591 take the digit and add 1 to get 6.
5 + 6 = 11.
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