[Please help...Giving Medal and Fan!]
Solve for x: e^(2x)=3x^2

Question

[Please help...Giving Medal and Fan!]
Solve for x: e^(2x)=3x^2

anonymous · Answer

First of all, try rearranging the equation into a log form.
As a tip, if $$e ^{a} = b$$ then $$a = \ln b$$

anonymous · Answer

I think this question will involve the use of the Lambert W function; for more information you can check out http://en.wikipedia.org/wiki/Lambert_W_function

anonymous · Answer

I don't think I can help much further, sorry

anonymous · Answer

its ok thanks for the tip

tkhunny · Answer

This is one of the great disappointments of the early study of mathematics.  Such a simple expression, but no solution in a finite number of steps or in any "closed form".  Sad, isn't it?

All is not lost.  There are numerical methods that do just fine.

Define: $f(x) = e^{2x} - 3x^2$ and find the zero of this function.  There are various ways to go about it.  A quick jaunt through Newton's Method gives, starting at x = 0, in only five iterations, x = -0.390646380802054.  It's a lovely exercise.