Question

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!!!

Answer 1

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

Answer 2

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

Answer 3

\[e^x-3=-e^{-x}\]

Answer 4

are you trying to solve for x?

Answer 5

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

Answer 6

\[e^x-3=-e^{-x}\]\[e^x-3+e^{-x}=0\]\[e^{2x}-3e^x+1=0\]

now substitute \(e^x=m\)

\[m^2-3m+1=0\]

solve this for m

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

quadratic formula?

Answer 12

to get x , just take the natural logarithm of m

Answer 13

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

Answer 14

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

Answer 15

@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? :-)

Answer 16

note that:
\[\cosh x=\frac 32\]\(\qquad\Downarrow\)\[x=\pm\operatorname{arccosh}\frac 32\]