What are the solutions tolog3x + log3(x2 + 2) = 1 + 2log3x?

The logarithms require x > 0. Subtract log₃ x from both sides to get log₃(x² + 2) = 1 + log₃ x = log₃(3x), so x² + 2 = 3x. Factoring gives (x − 1)(x − 2) = 0, and both positive solutions are valid: x = 1 and x = 2.

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