Q3 of 53 Page 36

Find all positive integers m,n such that (3m)n = 3m × 3n.

(3m)n = 3m × 3n

⇒ 3mn = 3m + n


Since the bases are same so the powers can be equated


mn = m + n


Let m = n


⇒ m2 = 2m


⇒ m = 2


Answer: m = 2, n = 2


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