If log_6 (x) + log_6 (x - 1) = 1, what is the value of x?
Show the answer and explanation
Correct answer
B. 3
Principle or equation
log_a M + log_a N = log_a (MN), and log_a b = c ⇔ a^c = b.
Why this answer is correct
log_6 [x(x-1)] = 1 → x(x-1) = 6^1 = 6 → x^2 - x - 6 = 0 → (x-3)(x+2)=0 → x=3 or x=-2. Since log arguments must be positive, x=3.
Example
Solve log_2 x + log_2 (x-2) = 3: x(x-2)=8 → x=4 (x=-2 invalid).
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.