1.

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

Answer»

LAWS of Indices:

1. am × aN = a{m + n}

2. a÷ 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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