Answer:
The error is at step (3) .
The correct step (3) will be,
[tex]\log_{b}(\frac {b^{x}}{b^{y}})[/tex]
= [tex]\log_{b}(b^{x - y})[/tex] [by using the laws of indices]
All other steps are correct.
Step-by-step explanation:
The error is at the step (3) , because the student has tried to prove the quotient rule of logarithms by using the property i.e., 'The quotient rule of logarithm' itself , i.e. ,by assuming the property does hold before proving it. So, the proof is fallacious.
The correct step (3) will be,
[tex]\log_{b}(\frac {b^{x}}{b^{y}})[/tex]
= [tex]\log_{b}(b^{x - y})[/tex] [by using the laws of indices]
All other steps are correct.
