Question

help me solve (e^x - e^-x)/2 = 2

Answer 1

I recommend you to try setting:
u=e^x

u^(-1)=e^(-x)

Answer 2

What do you mean? :S

Answer 3

A substitution might simplify your equation:

\[u=e^x\]
and therefore:

\[u^{-1 }=\frac{ 1 }{ u }=e^{-x }\]

Answer 4

Sorry my keyboard isn't configured to this system, hard for me to type things out on LaTeX. but if you perform this substituion, you should be able to solve the equation.

Answer 5

\[e^x-e^{-x}=4\] the multiply by \(e^x\) to get
\[e^{2x}-1=4e^x\] or
\[e^{2x}-4e^x-1=0\] solve the quadratic equation
\[u^2-4u-1=0\]

Answer 6

you should get
\[u=2\pm\sqrt{5}\] and then \(e^x\) cannot be negative, so it is
\(x=\ln(2+\sqrt{5})\)

Answer 7

How did you got the sqrt(5) ????

Answer 8

@satellite73