Posted by **Heather** on Sunday, January 6, 2013 at 3:23pm.

solve the inequality

e^x+e^x-x=6

can you show work

- calculus -
**Reiny**, Sunday, January 6, 2013 at 3:26pm
You don't have an inequality, you have an equation

Why do you have two terms the same?

Is there a typo ?

- calculus -
**Heather**, Sunday, January 6, 2013 at 5:22pm
I am sorry.

This is the equation.

Solve the follow exponential equation

e^x+e^-x=6

- calculus -
**Damon**, Sunday, January 6, 2013 at 6:55pm
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

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