Thread: 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)

I used my calculator to find the solution to the equation

solve ln(x)-e^(-x) =0 - Wolfram|Alpha

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.