solution:::
2lnx+2lny=1
=> 2lny= 1 - 2lnx
taking log with base 2 on both sides
ln y = log2 (1 - 2lnx )
=> y = elog2 (1 - 2^lnx )
from 2lnx , we get x > 0 ---(1)
from log2 (1 - 2lnx ), we get 1- 2lnx >0
=> 2lnx < 1
=>2lnx < 20
=> lnx < 0
=>ln x < ln 1
=> x < 1 ----(2)
from, (1) & (2), we get x

(0,1) ans.
P.S. initially, i did some mistake in takin the inequality...