Question

If 2^x – 2^{x– 1} = 4, then what is the value of 2^x + 2^{x– 1}?

(a) 8 

(b) 12 

(c) 10 

(d) 16

Answer 1

(b) 12

2^x - 2^x-1 = 4 ⇒ 2^x -\(\frac{2^x}{2}\) = 4 

⇒ 2^x\(\big(1-\frac12\big)\) = 4 ⇒ 2^x x \(\frac12\) = 4

⇒ 2^x = 8 ⇒ 2^x = 2³ ⇒ x = 3

∴ 2^x + 2^x-1 = 2³ + 2² = 8 + 4 = 12.