Solve the logarithmic equation: log₂(x) + log₂(x - 2) = 3?

A x = 4 only

B x = -2 only

C x = 4 and x = -2

D No real solution

✓ Correct Answer: Option A

Combine logarithms: log₂(x(x-2)) = 3. Convert to exponential form: x(x-2) = 2³, which simplifies to x² - 2x - 8 = 0. Factoring gives (x-4)(x+2)=0, so x=4 or x=-2. However, x must be > 2 for the original logarithms to be defined, so x=4 is the only solution.

💡 Why is A) the correct answer?

The correct answer to the question "Solve the logarithmic equation: log₂(x) + log₂(x - 2) = 3?" is Option A: x = 4 only.

The other options — B) x = -2 only, C) x = 4 and x = -2, D) No real solution — are incorrect for this CLEP Exam Prep question. As explained above: Combine logarithms: log₂(x(x-2)) = 3. Convert to exponential form: x(x-2) = 2³, which simplifies to x² - 2x - 8 = 0. Factoring gives (x-4)(x+2)=0, so x=4 or x=-2. However, x must be > 2 for the origi…

📚 About This CLEP Exam Prep Practice Question

This 3-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 logarithmic equation: log₂(x) + log₂(x - 2) = 3?

✓ Correct Answer: Option A

📚 About This CLEP Exam Prep Practice Question

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