Question

If 5^{3a – 1} × 125 = 25^{2a – 1}, then find the value of a.
1. 2
2. 4
3. 3
4. 1

Answer 1

Correct Answer - Option 2 : 4

Given:

5^{3a – 1} × 125 = 25^{2a –} 1

Concept:

A^x × A^y = A^{x + y}

If B^p = B^q, then p = q

Calculation:

5^{3a – 1} × 125 = 25^{2a – 1}

⇒ 5^{3a – 1} × 5³ = 5^{2(2a – 1)}

⇒ 5^{3a – 1 + 3} = 5^{4a – 2}

⇒ 5^{3a + 2} = 5^{4a – 2}

Now, B^p = B^q

⇒ 3a + 2 = 4a - 2

⇒ 4a – 3a = 2 + 2

⇒ a = 4

∴ The value of a is 4.