Identify the error in the student solution shown below. Find the correct answer.

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.