Let x and y be positive real numbers that satisfy (\log x)^2+(\log y)^2=\log \left(x^2\right)+\log \left(y^2\right). Compute the maximum possible value of (\log x y)^2.
Let x and y be positive real numbers that satisfy (\log x)^2+(\log y)^2=\log \left(x^2\right)+\log \left(y^2\right). Compute the maximum possible value of (\log x y)^2.