Question

If (300)⁸ = 65.61 × 10^x, then find the value of x.
1. 16
2. 18
3. 20
4. 14

Answer 1

Correct Answer - Option 2 : 18

Given:

(300)⁸ = 65.61 × 10^x

Concept:

If a^x = a^y, then x = y

Calculation:

(300)⁸ = 65.61 × 10^x

⇒ (3 × 100)⁸ = (6561/100) × 10^x

⇒ 6561 × 10¹⁶ = 6561 × 10^{x – 2}

⇒ 10¹⁶ = 10^{x – 2}

Now 16 = x – 2

⇒ x = 18

∴ The value of x is 18.