If 2x – 2x– 1 = 4, then what is the value of 2x + 2x– 1?(a) 8�

1.	If 2x – 2x– 1 = 4, then what is the value of 2x + 2x– 1?(a) 8 (b) 12 (c) 10 (d) 16
Answer» (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.

If 2x – 2x– 1 = 4, then what is the value of 2x + 2x– 1?(a) 8 (b) 12 (c) 10 (d) 16

Answer»

(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.