Solve for x, if:

   3
  x
 x
x    = 3

An algebraic solution is sought!

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