College Algebra CLEP Prep Practice 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