SOLUTION: how to solve this equation? x + ln (x^(2+x)) = 0 Thank you very much.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: how to solve this equation? x + ln (x^(2+x)) = 0 Thank you very much.      Log On


   

Question 754931: how to solve this equation?
x + ln (x^(2+x)) = 0
Thank you very much.
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
First we rewrite



ln+%28x%5E%282%2Bx%29%29+=+-x
Immediately we notice that no matter what we do we end up with exponential/logarithmic term as well as algebraic terms. This equation cannot be solved using algebra because it is neither strictly algebraic nor exponential and so no operations can be done to solve directly for x. In cases like this we can use numerical or graphic methods:

+graph%28+300%2C+300%2C+-1%2C+2%2C+-2%2C+2%2C+-x%2C+ln%28x%5E2%2Bx%29%29+


After tinkering with the window settings and such we can approximate the intersection as much as we need.
x is about 0.75941



:)