If 3^(2x - 1) = 27^(x - 2), find the value of x.
Answer and explanation
Correct answer: B. 5
- Step 1: Express both sides in base 3: 27 = 3^3, so 27^(x - 2) = (3^3)^(x - 2) = 3^(3x - 6).
- Step 2: Equate the exponents since bases are equal: 2x - 1 = 3x - 6.
- Step 3: Solve for x: -1 + 6 = 3x - 2x => x = 5.
Answer
5.
Why not the others: Option 4 forgets to distribute 3 to -2, setting 3x - 2 = 2x - 1 => x = 1. Option 3 is an arithmetic error. Option 7 adds 6 and 1.
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