Question

What will come in place of question mark (?) in the following question?

8^{(4x + 3)} = 64^{(3x + 1)}, then (2x + 3) = ?
1. 3
2. 4 
3. 6
4. 5

Answer 1

Correct Answer - Option 2 : 4 

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

Calculations:

Now,

8(4x + 3) = 64(3x + 1)

⇒ 8(4x + 3) = (8 × 8)(3x + 1)

⇒ 8(4x + 3) = 82(3x + 1)

Comparing powers 

⇒ 4x + 3 = 6x + 2

⇒ 2x = 1

⇒ x = 1/2

2x + 3 = 2 × (1/2) + 3

⇒ 1 + 3

⇒ 4

∴ The value of (2x + 3) is 4.