If log₂(x) + log₂(x - 2) = 3, what is the value of x?
Correct: C
Using the properties of logarithms, we have log₂(x(x - 2)) = 3. This means x(x - 2) = 2^3 = 8. So x^2 - 2x = 8, or x^2 - 2x - 8 = 0. Factoring, we get (x - 4)(x + 2) = 0. Therefore, x = 4 or x = -2. Since the logarithm of a negative number is undefined, x must be 4. We have to verify the solutions in the original equation. log₂(4) + log₂(4 - 2) = log₂(4) + log₂(2) = 2 + 1 = 3.