Can the Implicit Equation k = (c^m - a^m) / (b^m - a^m) be Solved Numerically?

[David1980]

Equation is:
k=(c^m-a^m)/(b^m-a^m)
where a, b, c, and k are constants. How to solve it (numerical?) Detail please.

Thanks

 

[maajdl]

Solve it with respect to what? m?
It could help you to assume:

x=exp(m)
a=exp(u)
b=exp(v)
c=exp(w)

you would solve for x, and with some luck it could be easy.
It would be almost like finding (positive) roots of a polynomial.