Given that log m = x + y and log n = x - y, express the value of log m²n in terms of x and y.

Given,

log m = x + y …….(i)

log n = x - y ……..(ii)

Multiplying (i) by 2 we get,

2log m = log m² = 2x + 2y ……(iii)

Adding (ii) and (iii) we get,

⇒ log m² + log n = 2x + 2y + (x - y)

⇒ log m²n = 3x + y.

Hence, log m²n = 3x + y.