Solve for x in the equation: 4^(2x - 1) = 32^(x + 1).

Answer and explanation

Correct answer: D. x = -7

  1. Step 1: Express both sides of the equation with a common prime base of 2.
  2. Step 2: 4 = 2^2, so 4^(2x - 1) = (2^2)^(2x - 1) = 2^(4x - 2).
  3. Step 3: 32 = 2^5, so 32^(x + 1) = (2^5)^(x + 1) = 2^(5x + 5).
  4. Step 4: Equate the exponents: 4x - 2 = 5x + 5.
  5. Step 5: Subtract 4x from both sides: -2 = x + 5.
  6. Step 6: Subtract 5: x = -7.
Answer
x = -7.
Why not the others: If x = -5, 2^(-22) != 2^(-20); if x = 3, 2^10 != 2^20; if x = 7, 2^26 != 2^40.

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