calculus
posted by Heather on .
solve the inequality
e^x+e^xx=6
can you show work

You don't have an inequality, you have an equation
Why do you have two terms the same?
Is there a typo ? 
I am sorry.
This is the equation.
Solve the follow exponential equation
e^x+e^x=6 
e^x = 1/e^x
so
e^x + 1/e^x = 6
e^2x/e^x + 1/e^x = 6
(e^2x + 1) = 6 e^x
let z = e^x
z^2 + 1 = 6 z
z^2  6 z + 1 = 0
z = [ 6 +/ sqrt(36 4) ] /2
z = 3 +/ .5 sqrt(32)
z = 3 +/ 2 sqrt 2
so
e^x = 5.828 or e^x = .1716
ln e^x = x = 1.76 or x = 1.76