I have a bunch of experimental data given by someone else which should fitting into the following form $$ y = A\exp(-b/(x-\mu)) $$
where $A$, $b$ and $\mu$ are constant but not known. I am thinking to use best fitting to figure out those parameters. What I did is to apply logrithm on both sides so the equation becomes $$ z = z_A - b/(x-\mu) $$ with $z= \log(y)$ and $z_A = \log(A)$. I am thinking it might be able to help if I could make this linear so by best fitting the data to a line I can figure out $b$ and $z_A$ by calculating the slope and intercept. However, it's not gonna work because $\mu$ is always there and not known. With matlab, I can type in the given $y$ and $x$ and use the cftool to fit those into a function of form $y = A\exp(-b/(x-\mu))$ and it will give me directly $A$, $b$ and $\mu$ directly. But I want to know if not using software, how can I simply the equation and solve it by hand?