(1/2)(logx + logy) = log{(x + y)/2} হলে নিচের কোনটি সঠিক?

প্রশ্ন: (1/2)(logx + logy) = log{(x + y)/2} হলে নিচের কোনটি সঠিক?

সমাধান:
(1/2)(logx + logy) = log{(x + y)/2}
⇒ (1/2)log(xy) = log{(x + y)/2}
⇒ log(xy)^1/2 = log{(x + y)/2}
⇒ (xy)^1/2 = (x + y)/2
⇒ xy = {(x + y)/2}²
⇒ xy = (x + y)²/4
⇒ 4xy = (x + y)²
⇒ 4xy = x² + y² + 2xy
⇒ x² + y² - 2xy = 0
⇒ (x - y)² = 0
⇒ x - y = 0
∴ x = y