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Powers of powers (Posted on 2004-05-11) Difficulty: 3 of 5
Solve for x, if:
   3
  x
 x
x    = 3
An algebraic solution is sought!

See The Solution Submitted by Federico Kereki    
Rating: 4.1000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Yikes-- spoiler present | Comment 3 of 11 |
(In reply to re: Yikes by SilverKnight)

I agree that right-to-left (upper-right to lower left) is the way, so that the spreadsheet can solve (after taking log of both sides twice) x^3*log(x) + log(log(x)) = log(log(3))

Having a cell in Excel for x^3 (as well as the other components),  and using Solver to equate the two sides, it shows that x^3 = 3.

Then it becomes obvious: when x is the cube root of 3, the top x^3 is 3; then the next one is also 3, and so on; it could actually go on for any number of levels.  At that point it is: aha! why didn't I think of that?


  Posted by Charlie on 2004-05-11 13:41:49
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