$$e^{A+B*\ln(x)}=m*e^{C+D*\ln(x)}+n,\qquad x \gt 0$$
I'm trying to solve for x in the equation above, but I am not sure where to even begin. If I take the natural log of both sides, I wind up with
$$A+B*\ln(x)=\ln(m*e^{C+D*\ln(x)}+n)$$
which is no nearer to solving it, and I don't know what to do next. I don't know of any natural log properties that would be applicable.
Is this equation possible to solve for x? If so, what's the best way to approach this?