I have got a system of non-linear equations of the form
$$A x_1^Be^{\frac{- C}{x_1}} = k_1$$$$A x_1^B \exp \bigg(\frac{- C}{x_1} \bigg) = k_1$$ $$A x_2^Be^{\frac{- C}{x_2}} = k_2$$$$A x_2^B \exp \bigg(\frac{- C}{x_2} \bigg) = k_2$$ $$A x_3^Be^{\frac{- C}{x_3}} = k_3$$$$A x_3^B \exp \bigg(\frac{- C}{x_3} \bigg) = k_3$$
where $[x_1, x_2, x_3]$ and $[k_1, k_2, k_3]$ are known. The couple of constants $[A, B, C]$ is the unknown.
I'd like to know what is the best way to solve this kind of problem involving a non-linear system of equations.
Thanks a lot.