Problem Solving (PS) | Re: The sum of the digits of 10^x−1 is equal to 3^8

10^x - 1 = 3^8

It is worth noting when starting this problem that 10-1 = 9, 10^2 - 1 = 99, etc. So whatever X equals, is how many 9s that number will have.

Also:
3^8 = (3^2)^4 = 9^4

So to find out what X is we need to determine how many 9's are in 9^4

Well, (9) (9^1) has only one 9
(9)*9 (9^2) has nine, 9s
(9)*9*9 (9^3) has eighty-one 9s
and (9)*9*9*9 (9^4) has 729 9s.

Thus 10^729 - 1 will have the same amount
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