Available: x/y > four

The original formula is simplified as lg(x+2y)(x-4y)=lg2xy.

So: (x+2y)(x-4y)=2xy.

Simplification: x2-4xy-8y 2 = 0, divided by y 2.

Get: (x/y) 2-4x/y-8 = 0 and get the solution: x/y=2+2√3, or x/y=2-2√3.

Because x/y >; 4, so x/y=2+2√3.