Question

If 4^{3a + 2} ÷ 4^2a = 4^{2a - 3}, then find the value of a.
1. 5
2. 4
3. 2
4. 3

Answer 1

Correct Answer - Option 1 : 5

Given:

43a + 2 ÷ 42a = 42a - 3

Concept:

A^x ÷ A^y = A^{x – y}

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

Calculation:

4^{3a + 2} ÷ 4^2a = 4^{2a – 3}

⇒ 4^{3a + 2 – 2a} = 4^{2a – 3}

⇒ 4^{a + 2} = 4^{2a - 3}

Now, Comparing exponents we'll get

a + 2 = 2a – 3

⇒ a = 3 + 2

⇒ a = 5

∴ The value of a is 5.