Solving a hyperbolic equation

Question

I have the following equation:
    Tanh[-19.4*[Zeta]]*Exp[k x] == Tanh[-19.4*[Psi]];
    [Zeta] = 66;
    k x = 9.21;

I want to calculate the value of [Psi] by using this above equation. I used the Solve command
 Solve[Tanh[-19.4*[Zeta]]*Exp[k x] == Tanh[-19.4*[Psi]], [Psi]]

But it shows the error like:
Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found;    use Reduce for complete solution information. >>
Question

How do I solve this equation.

Please help me. Thank You

chris · Answer

Replacing  -19.4 with $sigma$ and solving yields
eqn = Tanh[-[Sigma]*[Zeta]]*Exp[k x] == Tanh[-[Sigma]*[Psi]]
Solve[eqn, [Psi]] // FullSimplify

which seems about right?

Daniel Huber · Answer

I assume that k x in k x =9.21 should read kx without space. Then it is a good idea to rationalize the constants. With this we get:
[Zeta] = 66;
kx = 921/100;
Solve[Tanh[-194/10*[Zeta]]*Exp[kx] == Tanh[-194/10*[Psi]], [Psi]]

or numerical:

Solving a hyperbolic equation

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