The table shows a student’s proof of the quotient rule for logarithms.
Let M = bx and N = by for some real numbers x and y.
Step Reason
1 Given
2 Substitution
3 Properties of logarithms
4 Logarithm property logb(bc) = c
5 Substitution
What is the error in the proof?
The error is in step 3. The reason should be the quotient property of exponents.
The error is in step 3. You cannot use a property of logarithms to prove that same property.
The error is in step 2. The reason should be the quotient property of exponents.
The error is in step 5. The student did not convert from exponential to logarithmic form correctly when solving for x and y.
