$\"\"$

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(a)

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The statement is $\"\"$ .

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Consider $\"\"$ .

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Simplify the expression.

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$\"\"$

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Consider $\"\"$ .

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Simplify the expression.

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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(b)

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The function are $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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Take natural logarithm on each side.

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$\"\"$

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Apply power rule of logarithm : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Now consider $\"\"$ .

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Take natural logarithm on each side.

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$\"\"$

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Apply power rule of logarithm : $\"\"$ .

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$\"\"$

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Observe the both the functions, conclude that $\"\"$ .

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Thus, the functions are not same $\"\"$ .

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$\"\"$

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(c)

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Thus, the derivative of $\"\"$ is $\"\"$ .

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$\"\"$

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Now consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Apply formula : $\"\"$ .

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$\"\"$

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$\"\"$

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Thus, the derivative of $\"\"$ is $\"\"$ .

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$\"\"$

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(a)

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$\"\"$ .

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(b)

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The functions are not same, $\"\"$ .

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(c)

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Derivative of $\"\"$ is $\"\"$ .

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Derivative of $\"\"$ is $\"\"$ .