Given:
$\ln(xa)= b\ln(c-x)$
I am unsure of how to manipulate the values within the natural logs to solve for x while the factor b remains. I can safely move in circles by applying the definition of the logarithm to yield the exponential form.
$ax = (c-x)^{b}$
Is there a way to make forward progress? I know all values ($a$, $b$, $c$, $x$) to be real and $b$ to be a positive integer. I am only interested in real solutions.