Solve for x (3^x = x^2)

  • Thread starter Benn
  • Start date
  • #1

Homework Statement

Find all possible values of x:

x2 = 3x

Homework Equations

The Attempt at a Solution

I took the log of both sides.. didn't get anywhere. I'm not sure where to start.

Answers and Replies

  • #2
You can't solve this analytically with logarithms. You can either guess the right answer and prove that it works, use the Lambert W function or you can use a numerical method.
  • #3
okays... thanks a lot!
  • #4
Your equation has a solution, because both functions are monotone and increasing.

[tex] 3^{-1}<(-1)^2 [/tex]

[tex] 3^0 > 0^2 [/tex]
  • #5
One simple way to find that solution is via a fixed point iteration. Taking the square root of both sides and recognizing that the solution is negative yields
This converges to the solution fairly quickly. Quickly by fixed point iteration standards, that is. Fixed point iteration is rarely fast.

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