Question

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 mc028-1.jpg Given
2 mc028-2.jpg Substitution
3 mc028-3.jpg Properties of logarithms
4 mc028-4.jpg Logarithm property logb(bc) = c
5 mc028-5.jpg 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.

Answer 1

The error is in step 3. The step that replaces b^x / b^y with b^{x-y} uses the quotient law for exponents (b^x / b^y = b^{x-y}), not a property of logarithms.