Find how many digits the base seven number 7^(7^7) has when written in base seven.
in base 7 , 7 is written ... 10 ... 1 * 7^1 + 0 * 7^0
... the numbering sequence is ... 1 , 2 , 3 , 4 , 5 , 6 , 10
translating to base 7 ... 10^(10^10) ... a one, followed by 7^7 zeros