College Algebra CLEP Prep Practice Exam

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Prepare for the College Algebra CLEP Test with our comprehensive practice exam. Study with flashcards and multiple choice questions, each offering clues and detailed explanations. Achieve your best score and excel in your exam!

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Solve the equation log3x + log3(x + 5) = 2 for x.

The correct answer is: 8

To solve this equation, we need to use the properties of logarithms to combine the two terms on the left side into one. Using the property log a + log b = log(ab), we can rewrite the equation as log3(x(x + 5)) = 2. Then, using the property log a^b = b log a, we can rewrite further as log3(x^2 + 5x) = 2. Now, using the definition of logarithms, we know that log a = b is equivalent to a = 10^b. So in our equation, 3^(x^2 + 5x) = 10^2, or 3^(x^2 + 5x) = 100. Using logarithms again, we can rewrite as x^2 + 5x = log3(100) = log3(10