# Thread: solve ln x = x - 2 for x

1. ## solve ln x = x - 2 for x

I can't figure it out. =/

$ln(x) = x - 2$
$x = e^{x - 2}$

$x = \frac{e^x}{e^2}$

I'm quite stuck. I feel like I should know how to do this, but just can't remember. >_<

2. You need to solve it numerically I'm afraid. Plotting it gives rough ideas of x= 0.16 and 3.13

3. How irksome. Thanks though.... >_< I detest having to use Newton's method.

4. Originally Posted by Zizoo
How irksome. Thanks though.... >_< I detest having to use Newton's method.
Use the Bisection Method then :P

5. Originally Posted by e^(i*pi)
You need to solve it numerically I'm afraid. Plotting it gives rough ideas of x= 0.16 and 3.13
Can be solved in closed form in terms of Lambert's W function (real (0) branch for a real solution):

$x=-\text{W}(-e^2)=0.158594$

CB