(log_4 x + log_4 y = 1 + log_4 9) and (log_2(x + y) = log_2 5 + 2)

1. Simplify the first equation: log_4(xy) = log_4(4*9) => xy = 36.
2. Simplify the second equation: log_2(x+y) = log_2(5*4) => x+y = 20.
3. Solve the system: x+y=20, xy=36. Substitute y=20-x into the second equation: x(20-x)=36 => 20x - x^2 = 36 => x^2 - 20x + 36 = 0. Using the quadratic formula, x = (20 ± sqrt(400 - 144))/2 = (20 ± sqrt(256))/2 = (20 ± 16)/2. So, x1 = 18, x2 = 2. If x=18, y=2. If x=2, y=18.
Answer: (18, 2) and (2, 18).