If 2^(2x + 1) - 9 * 2^x + 4 = 0, what are the solutions for x?
Answer and explanation
Correct answer: B. x = 2 and x = -1
- Step 1: 2 (2^x)^2 - 9(2^x) + 4 = 0. Let y = 2^x > 0: 2y^2 - 9y + 4 = 0. Step 2. Factor: (2y - 1)(y - 4) = 0 => y = 4 or y = 1/2. Step 3. 2^x = 4 => x = 2; 2^x = 1/2 => x = -1. Answer: x = 2 and x = -1. Why not the others:* y = 4 and y = 1/2 are values of 2^x, not x.
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