SOLUTION: Find how many digits the base ten number 9^(9^9) has when written in base nine.

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Question 1133989: Find how many digits the base ten number 9^(9^9) has when written in base nine.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

9%5E%289%5E9%29
it will have 9%5E9%2B1 digits = 387420490+digits (base+10)
If the number of digits was expressed in base 9 it would look bigger.

I can do the conversion if you want:
387420490%2F9 = 43+046+721 Rhighlight%281%29
43046721%2F9= 4+782+969 Rhighlight%280%29
4782969%2F9 = ++531+441 Rhighlight%280%29
531441%2F9 = 59049 Rhighlight%280%29
59049%2F9 = 6561 Rhighlight%280%29
6561%2F9 = 729 Rhighlight%280%29
729%2F9 = 81 Rhighlight%280%29
81%2F9 = 9+ Rhighlight%280%29
9%2F9+ = 1 Rhighlight%280%29
1%2F9+ = 0 Rhighlight%281%29

So the number of digits base 9 is 1+000+000+001.

so, 9%5E%289%5E9%29 base 10 will be 1+000+000+001 base 9 units long in base 9.