If 2^(2x + 3) − 2^(x + 2) = 112, what is the value of x?

Correct answer: c 2

With 2^x = a, 8a² − 4a = 112, 2a² − a − 28 = 0, (a − 4)(2a + 7) = 0; a = 4 (a > 0), so 2^x = 4 and x = 2.

Why the other options are wrong

• a 4: At x = 4 the left side is 2^11 − 2^6 = 2048 − 64 = 1984, not 112.
• b 7/2: At x = 7/2 the left side is 2^10 − 2^5.5 ≈ 978.7, not 112.
• d − 7/2: At x = −7/2 the left side is 2^(−4) − 2^(−1.5) ≈ −0.29, not 112.