Solving $\frac{\ln(x)\ln(y)}{\ln(1-x)\ln(1-y)}=1$ for $y$ 
I'm trying to solve for $y$ in terms of $x$ for the expression below.
$$\frac{\ln(x)\ln(y)}{\ln(1-x)\ln(1-y)}=1$$

First I multiplied both sides by $$ \frac{\ln(1-x)}{\ln(x)} $$
to get
$$ \frac{\ln(y)}{\ln(1-y)}=\frac{\ln(1-x)}{\ln(x)} $$
but I don't see how to isolate $y.$ I tried using every technique I know including logarithm properties.

Because, in the general case, the equation depends on two algebraically independent monomials ($\ln(y),\ln(1-y))$, the equation cannot be solved for $y$ by only rearranging it by applying only finite numbers of elementary functions/operations.
Other tricks, Special functions, numerical or series solutions could help.
