Question

How do you solve:
e^–x + xe^–x = 0.123?

Answer 1

factor e^-x

Answer 2

\[e^{-x}(1+x)=0,123\]
introduce ln

Answer 3

when we use ln, does it become
-x(1+x)=ln(0.123) ?

Answer 4

it becomes : \[\large -x+\ln(x+1)=\ln(0.123)\]

i don't know what to do from there.

Answer 5

using log n then differentiate

Answer 6

\[-x +\ln (1+x)=\ln 0,123\]

Answer 7

you could solve this numerically.

Answer 8

how

Answer 9

newton;s method for approximation might help maybe,,but its quite tedious..

Answer 10

woaaah?

Answer 11

newton's method works fine. But wolfram is easier, unless you have to solve this by hand

Answer 12

http://www.wolframalpha.com/input/?i=e^-x%2Bx*e^-x%3D0.123

Answer 13

http://www.wolframalpha.com/input/?i=x%2B1%3D0.123e%5Ex

Answer 14

If you wanted to do it with a program, here is an example.
The difficult part is knowing where to start the search for the 2 roots, so plotting the function is helpful.