Express log_b(x^3 / y^2) in terms of log_b(x) and log_b(y).

A 3log_b(x) + 2log_b(y)

B 2log_b(x) - 3log_b(y)

C 3log_b(x) - 2log_b(y)

D (log_b(x))^3 / (log_b(y))^2

✓ Correct Answer: Option C

Using logarithm properties, log_b(A/B) = log_b(A) - log_b(B) and log_b(A^n) = n log_b(A). Therefore, log_b(x^3 / y^2) simplifies to 3log_b(x) - 2log_b(y).

💡 Why is C) the correct answer?

The correct answer to the question "Express log_b(x^3 / y^2) in terms of log_b(x) and log_b(y)." is Option C: 3log_b(x) - 2log_b(y).

The other options — A) 3log_b(x) + 2log_b(y), B) 2log_b(x) - 3log_b(y), D) (log_b(x))^3 / (log_b(y))^2 — are incorrect for this CLEP Exam Prep question. As explained above: Using logarithm properties, log_b(A/B) = log_b(A) - log_b(B) and log_b(A^n) = n log_b(A). Therefore, log_b(x^3 / y^2) simplifies to 3log_b(x) - 2log_b(y).

📚 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.

Practice CLEP Exam Prep Quizzes → Browse All Questions Study Flashcards

Express log_b(x^3 / y^2) in terms of log_b(x) and log_b(y).

✓ Correct Answer: Option C

📚 About This CLEP Exam Prep Practice Question

Related CLEP Exam Prep Questions