Question

Identify the error in the student solution shown below and find the correct answer.

(2ln(x) = ln(3x) - (ln(9) - 2ln(3)))

a) (ln(x²) = ln(3x) - 0)
b) (ln(x²) = ln(3x/0)) - Division by 0, undefined
c) (ln(x²) = ln(3x))
d) (ln(x²) = ln(3x) + (ln(9) - 2ln(3)))

Answer 1

The error in the student solution is dividing by zero in the denominator, which is undefined. The correct answer is 2ln(x) = ln(3x) - ln(3²).

Step-by-step explanation:

The error in the student solution is option b) (ln(x²) = ln(3x/0)) - Division by 0, undefined.

The correct answer is option c) (ln(x²) = ln(3x)).

The error in the student solution is that they divided by zero in the denominator, which is undefined. In logarithms, division is represented by subtracting the logarithms of the two numbers. In this case, the correct equation would be 2ln(x) = ln(3x) - ln(3²).