Given f(mn ) = f(m) f(n) and f(24) = 54⇒ f (24) = 2 × 3 × 3 × 3⇒ f(2 × 12) = f(2) f(12) = f(2) f(2 × 6)= f(2)f(2) f(6) = f(2) f(2) f(2 × 3)= f(2) f(2) f(2) f(3) = 2 × 3 × 3 × 3Given that f(1). f(2) and f(3) are all positive integers hence by comparison, we getf(2) = 3 and f(3) = 2Hear we may safely consider f(1) = 1Now, f(18 ) = f(2) (9) = f(2) f(3 × 3)= f(2) f(3) f(3) = 3 × 2 × 2 = 12.