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Correct Answer:

The error in the student's solution is the attempt to apply the quotient property of logarithms to the constant 0. Since 0 is not a logarithm, the expression ln(3x) 0 cannot be written as a quotient of logarithms; it simply simplifies to ln(3x). Correct solution: ln(x^2) ln(3x) x^2 3x x^2 3x 0 x(x 3) 0 x 0, x 3 Since the domain of a natural logarithm is x > 0, x 0 is an extraneous solution. The correct answer is x 3.