Question

how do you solve e^x = x

Answer 1

by taking ln for both sides

Answer 2

Use Newton-raphson method

Answer 3

what is the newton-raphson method?

Answer 4

taking the ln does not anything

Answer 5

please help nowhereman

Answer 6

there is no analytic solution, so you should use an approximation method like Newton's tangent method

Answer 7

how do you know there is no analytic solution?

Answer 8

you're right. ln does not solve the problem

Answer 9

oh wait, there is no solution at all, because \[ e^x >= 1 + x \]

Answer 10

ya, e^x always larger than x, so e^x = x does not have any solution

Answer 11

you are wrong. The answer is nonreal, which i am well aware of. I know what the number is to many decimal places. (Just take the ln of any number over and over again), but i have no idea how to find the number.

Answer 12

you have to iterate using computer methods to find this value

Answer 13

can you prove that?

Answer 14

If you use the moivre's theorem you know that e^(ix) = isinx + cosx or something like that

Answer 15

I used software program and found that
x=-W(-1), where W(z) is the product log function

Answer 16

what software did you use? did u use wolfram alpha? what is the product log function?

Answer 17

yes.. here is the definition of the function
http://www.wolframalpha.com/input/?i=product+log+function

Answer 18

ok