Question

2^{x - 1} + 2^{x + 1} = 320. Find the value of x.
1. 6
2. 7
3. 8
4. 9

Answer 1

Correct Answer - Option 2 : 7

Given:

2x - 1 + 2x + 1 = 320. We have to find the value of x.

Calculation:

2x - 1 + 2x + 1 = 320

⇒ 2^x/2 + 2^x × 2 = 320

⇒ 2^x(1/2 + 2) = 320

⇒ 2^x × (5/2) = 320

⇒ 2^x = 320 × (2/5)

⇒ 2^x = 64 × 2

⇒ 2^x = 128

⇒ 2^x = 2⁷

⇒ x = 7

∴ The required value of x is 7.