Is there a way to find the equation of the curved part for this:
$$\frac{1}{2^x}-\frac{1}{3^x}=\frac{1}{2^y}-\frac{1}{3^y}$$ for $x$? See WolframAlpha for the plot.
The curve is crossing the line $y=x$ at $x=\log_{\frac{3}{2}}(\log_2(3))$
I tried several cases in geogebra, but without success. I don't even know if something fits.
Edit: This equation is very similar to $x^y=y^x$. I guess I'll end-up with a Lambert $W$ function.