Solve the equation for x: 9^(2x-1) = 27^(x+2)

A x = 8

B x = 4

C x = -8

D x = -4

✓ Correct Answer: Option A

Rewrite with a common base: (3^2)^(2x-1) = (3^3)^(x+2). This simplifies to 3^(4x-2) = 3^(3x+6). Equating exponents: 4x - 2 = 3x + 6. Solving for x yields x = 8.

💡 Why is A) the correct answer?

The correct answer to the question "Solve the equation for x: 9^(2x-1) = 27^(x+2)" is Option A: x = 8.

The other options — B) x = 4, C) x = -8, D) x = -4 — are incorrect for this CLEP Exam Prep question. As explained above: Rewrite with a common base: (3^2)^(2x-1) = (3^3)^(x+2). This simplifies to 3^(4x-2) = 3^(3x+6). Equating exponents: 4x - 2 = 3x + 6. Solving for x yields x = 8.

📚 About This CLEP Exam Prep Practice Question

This 2-level CLEP Exam Prep question from the College Algebra topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free CLEP Exam Prep practice test or use flashcards for spaced repetition review.

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Solve the equation for x: 9^(2x-1) = 27^(x+2)

✓ Correct Answer: Option A

📚 About This CLEP Exam Prep Practice Question

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