krikre wrote:
Could you please clarify how to calculate this in a bit more comprehensive way?
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 of 9's as 9^4