# Thread: Find the point of intersection of ln(x) and e^-x

1. ## Find the point of intersection of ln(x) and e^-x

So I'm trying to find the area of the region bounded by those two. I know how to set up the integral and everything, except I can't figure out what the point of intersection is so I can split up the integral into two integrals.

what does x = when ln(x)=e^-x?

Thanks!

PS. I'm using Maple and setting the 2 equal to each other I get {x = exp(RootOf(_Z*exp(exp(_Z))-1))} (I have no idea what that means and where the Z's come from)

2. ## Re: Find the point of intersection of ln(x) and e^-x

I used my calculator to find the solution to the equation $e^{-x} - \ln{x} = 0$

$x \approx 1.3097996...$

4. ## Re: Find the point of intersection of ln(x) and e^-x

Thanks guys. I got it using Wolfram, I was wondering if there's a method that I should know. I'm trying to use the least amount of shortcuts possible so I absorb all of the methods. Wolfram is incredible though.

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### intersection exp x , 3*x

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