Question

5^X-2 *3 ^X-2 EQUALS TO 135

Answer 1

Answer :

Now,

5^(x - 2) × 3^(x - 2) = 135

⇒ 5^x × 5^(-2) × 3^x × 3^(-2) = 135

⇒ (5^x × 3^x) × (5 × 3)^(-2) = 135

⇒ (5 × 3)^x × (5 × 3)^(-2) = 135

⇒ 15^x × 15^(-2) = 135

⇒ 15^x = 135 × 15²

⇒ 15^x = 135 × 225

⇒ 15^x = 30375

Taking log to both sides, we get

x log15 = log (30375)

⇒ x = (log30375)/(log15)

⇒ x = log(15³ × 9)/(log15)

∴x = log(15³ × 9)/(log15)

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