Solve for x: 9^x - 10 * 3^x + 9 = 0.
Answer and explanation
Correct answer: B. x = 0 and x = 2
- Step 1: Substitute u = 3^x, so 9^x = (3^2)^x = u^2. The equation becomes u^2 - 10u + 9 = 0. Step 2. Factor: (u - 1)(u - 9) = 0 => u = 1 or u = 9. Since u = 3^x: 3^x = 1 => x = 0; 3^x = 9 => x = 2. Answer: x = 0 and x = 2. Why not the others: Stopping at u = 1 and u = 9 fails to solve for the original variable x.
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