Solve for c , $y = x + c \big( \frac{mx}{c} + s \big)^a$ I get this equation 
$y = x + c \big( \frac{mx}{c} + s \big)^a$
how can I get the $c$ or $m$ ?
I try with $\ln$
$\ln\big(\frac{y-x}{c}\big) = a \ln \big( \frac{mx}{c} + s\big)$ 
and now ? 

Here is how you solve for $m$:
\begin{align*}
\frac{y-x}{c}=\left(\frac{mx}{c}+s\right)^{a}\\
\left(\frac{y-x}{c}\right)^{\frac{1}{a}}=\left(\frac{mx}{c}+s\right)\\
\left(\frac{y-x}{c}\right)^{\frac{1}{a}}-s=\frac{mx}{c}\\
\end{align*}
Hence
\begin{align*}
m=\frac{c}{x}\left(\left(\frac{y-x}{c}\right)^{\frac{1}{a}}-s\right)
\end{align*}
I think to solve $c$, you have to use numerical method since it is not explicit.
