SOLUTION: How many digits does 2^15 * 5^8 have when expanded?

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.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
11 digits
12 800 000 000
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