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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)

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Yikes | Comment 1 of 11
The order of operations for nested powers is to work your way up right?

x^x^x^3 = (((x^x)^x)^3)
but not (x^(x^(x^3))) [which tends to be much bigger.]

So the equation can be simplified to x^(3x^2) = 3
(I can get a solution of x=1.259615106 on my calculator, but this isn't an algebraic solution.)

Sometimes logarithms help but then you just get
3x^2 log(x) = log(3)

Ok, I'm stumped.

  Posted by Jer on 2004-05-11 09:42:02
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