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Find the value of (x – y), if (35)x ÷ (9)2x – 1 = 243 and (5)x – 2y × (5)x + y = 625.1). 02). 13). 24). 3 |
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Answer» LAWS of Indices: 1. am × aN = a{m + n} 2. am ÷ an = a{m – n} 3. (am)n = amn 4. (a)-m = 1/am 5. (a)m/n = n√am 6. (a)0 = 1 Given, (35)x ÷ (9)2x – 1 = 243 ⇒ (3)5X ÷ (32)2x – 1 = (3)5 ⇒ (3)5x ÷ (3)4x – 2 = (3)5 ⇒ (3){5x – 4x + 2} = (3)5 ⇒ (3)x + 2 = (3)5 Equating POWERS, ⇒ x + 2 = 5 ⇒ x = 5 – 2 = 3 Also, (5)x – 2y × (5)x + y = 625 ⇒ (5)(x – 2y + x + y) = (5)4 ⇒ (5)2x – y = (5)4 Equating powers, ⇒ 2x – y = 4 Substituting for ‘x’, ⇒ 2(3) – y = 4 ⇒ y = 6 – 4 = 2 ∴ (x – y) = 3 – 2 = 1 |
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