$\"\"$

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Observe the graph:

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The function is $\"\"$ .

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(a) Solve for $\"\"$ in the equation $\"\"$ .

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$\"\"$

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$\"\"$

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Definition of logarithmic function: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b) The function $\"\"$ .

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Area $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Area of the function $\"\"$ in terms of $\"\"$ is $\"\"$ .

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$\"\"$

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(c) Graph the area function.

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Graph of $\"\"$ :

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$\"\"$

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Observe the graph,

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Maximum area of the function occurs at $\"\"$

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Maximum area is $\"\"$ .

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$\"\"$

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(d) Graph the function $\"\"$ .

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Graph of the function $\"\"$ :

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$\"\"$

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Observe the graph,

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As $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) Area of the function $\"\"$ in terms of $\"\"$ is $\"\"$ .

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(c)

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$\"\"$

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Maximum area is 4.591.

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(d)

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$\"\"$

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$\"\"$ and $\"\"$ .