$\"\"$

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The function is $\"\"$ .

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The transformation function is $\"\"$ .

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Change of base formula : $\"\"$ .

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$\"\"$

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$\"\"$

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Vertical shrink : $\"\"$ , shrink the graph of $\"\"$ vertically by a factor of $\"\"$ .

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$\"\"$ shrinks the graph of $\"\"$ vertically by a factor $\"\"$ , where the value of $\"\"$ depends on the values of $\"\"$ .

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$\"\"$

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Case 1 :

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Check the logarithm function $\"\"$ for $\"\"$ .

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For an example, consider $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ shrinks the graph of $\"\"$ vertically by a factor of $\"\"$ .

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$\"\"$

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Case 2 :

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Check the logarithm function $\"\"$ for $\"\"$ .

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For an example, consider $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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Property of logarithm : $\"\"$ .

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$\"\"$

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Reflect the graph : $\"\"$ , reflect the graph of $\"\"$ about the $\"\"$ -axis.

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$\"\"$ reflect the graph of $\"\"$ about the $\"\"$ -axis and shrinks vertically by a factor of $\"\"$ .

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$\"\"$

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$\"\"$ shrinks the graph of $\"\"$ vertically by a factor $\"\"$ .