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Solving Tanh[x]=Tanh[a]Tanh[b x + c]

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  • Subject: [mg83424] Solving Tanh[x]=Tanh[a]Tanh[b x + c]
  • From: Yaroslav Bulatov <yaroslavvb at>
  • Date: Tue, 20 Nov 2007 03:49:22 -0500 (EST)

I'd like to use Mathematica to show that solution of Tanh[x] - Tanh[a]
Tanh[b x + c]=0 can be written as
1/2 Log (Root[c1 x^(1+b) + c2 x^b + c3 x -1]) for certain coefficients
c1,c2,c3 when b is a positive integer

Tanh[x] - Tanh[a] Tanh[b x + c]// TrigToExp // Together // Numerator
gives me almost what I need, except now I need to factor out Exp[2x]
as a separate variable. What's the best way of achieving it? Using
syntactic replacement rules like {Exp[a_+b_]->Exp[a]Exp[b],Exp[2x]->x}
seems like an uphill battle against the evaluator which automatically
simplifies Exp expressions


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