Solve for x in the exponential relation: 3^(2x - 1) = 27^(x - 2).
Answer and explanation
Correct answer: A. x = 5
- Step 1: Express 27 as a power of 3: 27 = 3^3, so 27^(x - 2) = 3^(3(x - 2)) = 3^(3x - 6). Step 2. Equate exponents: 2x - 1 = 3x - 6. Step 3. Rearrange: -1 + 6 = 3x - 2x => x = 5. Answer: x = 5. Why not the others: x = 4 misses the distribution of 3 across (x - 2); x = 6 or 3 result from sign flips.
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