Solve for x in the exponential equation 4^(x + 1) - 10 * 2^x - 24 = 0.
Answer and explanation
Correct answer: D. x = 2
- Step 1: Note 4^(x + 1) = 4 (2^x)^2. Let y = 2^x > 0. Step 2. The equation becomes 4y^2 - 10y - 24 = 0, or 2y^2 - 5y - 12 = 0. Step 3. Factor: (2y + 3)(y - 4) = 0. Since y > 0, y = 4. Step 4. 2^x = 4 => x = 2. Answer: x = 2. Why not the others:* Check x = 2: 4^3 - 10(4) - 24 = 64 - 40 - 24 = 0.
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