SOLUTION: Find how many digits the base seven number 7^(7^7) has when written in base seven.

Question 1134631: Find how many digits the base seven number 7^(7^7) has when written in base seven.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The number 7^(7^7) does not exist in base 7; the largest digit in base 7 is 6.

I assume the question you are really asking is how many digits the BASE 10 number 7^(7^7) has when written in base 7.

The number n^x when written in base n has (x+1) digits:
10^3 in base 10 = 1000 (1 plus 3 zeros = 4 digits)
10^7 in base 10 = 10000000 (1 plus 7 zeros = 8 digits)
2^4 in base 2 = 16 in base 2 = 10000 (1 plus 4 zeros = 5 digits)
etc.,etc.

7^7 in BASE 10 = 823543; so the BASE 10 number 7^(7^7) has 823544 digits when written in base 7 (1 followed by 823543 zeros)
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