Let f be a function such that f (mn) = f (m) f (n) for every positive

1.	Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals (type in box)
Answer» Calculation: Let the value of f(2) and f(3) be ‘x’ and ‘y’ respectively, ⇒ f(24) = f(8).f(3) = f(2).f(2).f(2).f(3) = 54 ⇒ x³y = 54 ⇒ x³y = 27 × 2 ⇒ x³y = 3³ × 2 On comparing, x = 3 and y = 2 ⇒ f(2) = 3 ⇒ f(3) = 2 ⇒ f(18) = f(9).f(2) = f(3).f(3).f(2) ⇒ f(18) = 2 × 2 × 3 ⇒ f(18) = 12 ∴ The value of f(18) equals 12.

Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals (type in box)

Answer»

Calculation:

Let the value of f(2) and f(3) be ‘x’ and ‘y’ respectively,

⇒ f(24) = f(8).f(3) = f(2).f(2).f(2).f(3) = 54

⇒ x³y = 54

⇒ x³y = 27 × 2

⇒ x³y = 3³ × 2

On comparing, x = 3 and y = 2

⇒ f(2) = 3

⇒ f(3) = 2

⇒ f(18) = f(9).f(2) = f(3).f(3).f(2)

⇒ f(18) = 2 × 2 × 3

⇒ f(18) = 12

∴ The value of f(18) equals 12.

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Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals (type in box)

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