## jennag 2 years ago E^x-3=-e^-x someone please help me figure out how to solve the exponential equation! I keep coming up with this being undefined!!!

1. whpalmer4

$e^{x-3} = -e^{-x}$Is that the equation? Are you doing exponentials with complex numbers?

2. jennag

No it is e^x - 3 = -e^-x

3. UnkleRhaukus

$e^x-3=-e^{-x}$

4. UnkleRhaukus

are you trying to solve for x?

5. jennag

Yes! I believe that's what you do when you are solving An exponential equation right?

6. UnkleRhaukus

$e^x-3=-e^{-x}$$e^x-3+e^{-x}=0$$e^{2x}-3e^x+1=0$ now substitute $$e^x=m$$ $m^2-3m+1=0$ solve this for m

7. jennag

Would it be sqrt 3m-1, and -sqrt 3m-1

8. jennag

Sorry I'm on my iPad so I. Not typing it correctly

9. UnkleRhaukus

i got $m=\frac{3\pm\sqrt5}{2}$

10. jennag

Woahhh, okay I'm way off! How did you come up with that?

11. UnkleRhaukus

12. UnkleRhaukus

to get x , just take the natural logarithm of m

13. jennag

Got it, was doing it wrong :-) thank you!!!!

14. UnkleRhaukus

ill check your final result when you get there, if you want

15. whpalmer4

@jennag just for your edification, there's a thing called the hyperbolic cosine function, $$\cosh x$$ which happens to be $\cosh x =\frac{e^x-e^{-x}}{2}$Your problem could have been written as $2 \cosh x = 3$Looks so cute and innocent, doesn't it? :-)

16. UnkleRhaukus

note that: $\cosh x=\frac 32$$$\qquad\Downarrow$$$x=\pm\operatorname{arccosh}\frac 32$