$\"\"$

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

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

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Rewrite the functions using above formula.

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$\"\"$

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$\"\"$

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Graph:

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Graph the functions $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph :

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The function $\"\"$ is stretch the graph of $\"\"$ vertically by a factor of $\"\"$ .

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The curves $\"\"$ and $\"\"$ are the reflections of the graphs of $\"\"$ and $\"\"$ about $\"\"$ line respectively.

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$\"\"$

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Graph:

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$\"\"$

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The function $\"\"$ is vertically stretched graph of $\"\"$ by a factor of $\"\"$ .

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The curves $\"\"$ and $\"\"$ are the reflections of the graphs of $\"\"$ and $\"\"$ about $\"\"$ line respectively.