If the solution curve $y=y(x)$ of the differential equation $y^2 d x+\left(x^2-x y+y^2\right) d y=0$, which passes through the point $(1,1)$ and intersects the line $\mathrm{y}=\sqrt{3} \mathrm{x}$ at the point $(\alpha, \sqrt{3} \alpha)$, then value of $\log _{\mathrm{e}}(\sqrt{3} \alpha)$ is equal to