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Is there a mathematical way to solve such equations, besides try and error of course?

$e^{-x} = 1-x/5$

user -1
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1 Answers1

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The solution is

$$ x = W(-5e^{-5})+5 $$

besides the solution $ x=0$.

Note: Lambert $W$ function is the solution of the equation

$$ W(t) e^{W(t)} = t. $$

science
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    Thanks for introducing me to Lambart Function...I was really baffled how you got $x = W(-5e^{-5})+5$ in the first place, I had to reverse engineer it to find out how...Thanks a lot – user -1 Mar 04 '15 at 04:24
  • @user3556914: You are very welcome! Happy to assist. – science Mar 04 '15 at 04:37