The table shows a student's proof of the quotient rule for logarithms.Let M = b* and N = by for some real numbers x and yWhat is the error in the proof?
Accepted Solution
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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.