The equation that i cannot solve is
(e^x + e^-x) / 2 = 4
Hint: The equation is quadratic in $\displaystyle e^x$
First multiply the equation by $\displaystyle 2e^{x}$ This gives
$\displaystyle (e^x)^2+1=8e^{x} \iff (e^{x})^2-8e^{x}+1=0$
If you want you can use the substition $\displaystyle u=e^{x}$ to get the quadratic
$\displaystyle u^2-8u+1=0$
Can you finish from here?