If log_3 (x) + log_3 (x - 8) = 2, what is the value of x?
Show the answer and explanation
Correct answer
A. 9
Principle or equation
Use the logarithm product rule: log_b A + log_b B = log_b (AB). Then convert to exponential form.
Why this answer is correct
Combine: log_3 [x(x - 8)] = 2. Thus x(x - 8) = 3^2 = 9. So x^2 - 8x - 9 = 0, giving (x - 9)(x + 1) = 0. Since x > 0 and x > 8, only x = 9 is valid.
Example
Solve log_2 (x) + log_2 (x - 2) = 3: x(x - 2) = 8, so x = 4.
This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.