anonymous
  • anonymous
how do you solve e^x = x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
by taking ln for both sides
anonymous
  • anonymous
Use Newton-raphson method
anonymous
  • anonymous
what is the newton-raphson method?

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anonymous
  • anonymous
taking the ln does not anything
anonymous
  • anonymous
please help nowhereman
nowhereman
  • nowhereman
there is no analytic solution, so you should use an approximation method like Newton's tangent method
anonymous
  • anonymous
how do you know there is no analytic solution?
anonymous
  • anonymous
you're right. ln does not solve the problem
nowhereman
  • nowhereman
oh wait, there is no solution at all, because \[ e^x >= 1 + x \]
anonymous
  • anonymous
ya, e^x always larger than x, so e^x = x does not have any solution
anonymous
  • anonymous
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.
anonymous
  • anonymous
you have to iterate using computer methods to find this value
anonymous
  • anonymous
can you prove that?
anonymous
  • anonymous
If you use the moivre's theorem you know that e^(ix) = isinx + cosx or something like that
anonymous
  • anonymous
I used software program and found that x=-W(-1), where W(z) is the product log function
anonymous
  • anonymous
what software did you use? did u use wolfram alpha? what is the product log function?
anonymous
  • anonymous
yes.. here is the definition of the function http://www.wolframalpha.com/input/?i=product+log+function
anonymous
  • anonymous
ok

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