e^x-x=0

Postby nklknll; » Fri Oct 25, 2013 2:47 pm
There are no solution.
e^x-x=0
e^x=x
e^x>0
e^0=1>0
e^0.5=1.65>0.5
e^1=e>1
e^2=7.39>2

e^x-x=0

Peter is absolutely correct - there is no solution.
This is just another way to look at this problem.

If you graph y = e^x - x

then e^x-x=0 when y=0 ( y=0 is the x axis)

In other words e^x - x = 0 when y = e^x - x crosses the x axis.

I used http://rechneronline.de/function-graphs/
to graph this.

It can be seen from the graph that e^x - x >= 1 for all values of x.

y equals exminusx.JPG

You could also have done this using calculus - you would get the same answer.