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

Answer 1

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?

Answer 2

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: