SOLUTION: Find how many digits the base ten number {{{7 ^ (7 ^ 7)}}} (That's 7 ^ (7 ^ 7) ) has when written in base seven.

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Question 1200558: Find how many digits the base ten number 7+%5E+%287+%5E+7%29 (That's 7 ^ (7 ^ 7) ) has when written in base seven.
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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Notice that  7^(7^7) = 7%5E823543.


It means that in base 7 the number  7^(7^7)   has the leading digit 1 followed by  7^7 = 823543  zeroes.


In all, in base 7 the number  7^(7^7)  has  1 + 823543 = 823544 digits.  ANSWER

Solved.