$\"\"$

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(a)

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The function is $\"\"$ .

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The function $\"\"$ is defined when $\"\"$ .

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Therefore, the domain of the function $\"\"$ is $\"\"$ .

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$\"\"$

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(b)

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The function is $\"\"$ .

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Rewrite the function as $\"\"$ .

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To find the inverse of a function interchange $\"\"$ and $\"\"$ terms.

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$\"\"$

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Defnition of logarithm : $\"\"$ if and only if $\"\"$ .

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$\"\"$

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$\"\"$ .

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The inverse function is $\"\"$ .

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$\"\"$

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(c)

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In the function $\"\"$ the $\"\"$ term lies between $\"\"$ and $\"\"$ .

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At $\"\"$ .

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Substitute $\"\"$ in the function.

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$\"\"$

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Power property of logarithm : $\"\"$ .

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$\"\"$

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Property of logarithm : $\"\"$ .

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$\"\"$

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For $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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(d)

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Since the function $\"\"$ is negative, consider $\"\"$ .

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$\"\"$

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Take exponent with base $\"\"$ on each side.

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$\"\"$

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Inverse property of logarithm : $\"\"$ .

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$\"\"$

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At $\"\"$ .

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$\"\"$

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Thus, the interval is $\"\"$ .

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$\"\"$

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(e)

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If the function is increased by a factor $\"\"$ , then consider the $\"\"$ term as $\"\"$ .

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Thus, the function $\"\"$ .

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$\"\"$

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Quotient property of logarithm : $\"\"$ .

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$\"\"$

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$\"\"$

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Thus, $\"\"$ must be raised by a factor $\"\"$ .

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$\"\"$

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(f)

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The functions are $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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Find the ratio between $\"\"$ to $\"\"$ .

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$\"\"$

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Thus, the ratio between $\"\"$ to $\"\"$ is $\"\"$ .

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$\"\"$

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(a) Domain of the function $\"\"$ is $\"\"$ .

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(b) The inverse of the function is $\"\"$ .

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(c) The interval of $\"\"$ is $\"\"$ .

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(d) The interval is $\"\"$ .

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(e) $\"\"$ must be raised by a factor $\"\"$ .

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(f) The ratio between $\"\"$ to $\"\"$ is $\"\"$ .