import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12b_2003_p17 (x y : ℝ) (h₀ : 0 < x ∧ 0 < y) (h₁ : Real.log (x * y ^ 3) = 1)
  (h₂ : Real.log (x ^ 2 * y) = 1) : Real.log (x * y) = 3 / 5 := by sorry