I know that $x e^x = e$ means $x = 1$, but how do you solve for it?
Solving the equation $x e^x = e$
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transcendental-equations
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2What have you tried? Can you rule out some ranges for $x$? Have you tried playing with logarithms (the natural thing to do)? – 2010-11-28
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6@Raskolnikov: the problem is to show that x = 1 is the only (say, real) solution. I do not think "duh" is a constructive comment. – 2010-11-28
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0So guys, correct me if I am wrong: In many ways we can *prove* that x = 1, but given "xexp(x) = e", it is impossible to solve for x, that is, write x = {some formula} = ... = 1. – 2010-11-28
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0@Perfecto: essentially, yes. – 2010-11-29
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0Are we going to debate the term "closed form" again? – 2010-11-29
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0You have to use a new function, the Lambert W function. Try it in Maple, Mathematica or Wolfram Alpha. – 2018-10-09