Question

The table shows a student's proof of the quotient rule for logarithms.

Answer 1

Answer:

The error is at step (3) .

The correct step (3) will be,

$\log_{b}(\frac {b^{x}}{b^{y}})$

= $\log_{b}(b^{x - y})$   [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,

$\log_{b}(\frac {b^{x}}{b^{y}})$

= $\log_{b}(b^{x - y})$   [by using the laws of indices]

All other steps are correct.