Which is the only solution to the equationlog3(x2 + 6x) = log3(2x + 12)?

Since both logarithms have the same base, their arguments must be equal: x² + 6x = 2x + 12. This gives (x + 6)(x − 2) = 0, so the possible solutions are x = −6 and x = 2. At x = −6, both logarithm arguments are 0, which is not allowed; at x = 2, both arguments are 16. Therefore, the only solution is choice D, x = 2.

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