Differential Equations

If the solution curve of the differential equation \(\left(y-2 \log _{e} x\right) d x+\left(x \log _{e} x^{2}\right) d y=0, x > 1\) passes through the points \(\left(e, \frac{4}{3}\right)\) and \(\left(e^{4}, \alpha\right)\), then \(\alpha\) is equal to ____________.