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- Oct 3rd 2009, 01:41 PM #1

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## 3-x=3e^(-x)

hello everyone, I am currently working on an assignment and have solved my problem down to the following:

3-x=3e^(-x)

I have graphed both functions and seen that a solution exists that is not 0 and I am lost as to how to find the exact solution.

If anyone can help that would be greatly appreciated.

thanks,

Eric

- Oct 3rd 2009, 02:42 PM #2

- Oct 3rd 2009, 03:42 PM #3

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- Oct 3rd 2009, 05:05 PM #4

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This isn't what skeeter (or I) would call an "elementary algebraic method" but:

Multiply both sides by : or . Now let y= x- 3 so that x= y- 3 and the equation becomes so .

Now use "Lambert's W function" which is**defined**as the inverse to the function f(x)= . In this case so that . That is, as I said, not an "elementary algebraic" method but it is as good a solution as "x= cos(3)" or "x= log(5)" would be.