$\"\"$

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Prove the Power property of logarithm using graphs.

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

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Consider the logarithm expression $\"\"$ .

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Apply power property of logarithm.

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$\"\"$ .

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Graph :

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Graph of the logarithm expression $\"\"$ .

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$\"\"$

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Graph of the logarithm expression $\"\"$ .

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$\"\"$

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Observe the two graphs both are same, so the Quotient property of logarithm proved.

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$\"\"$

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Prove the power property of logarithm using equations.

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Consider a equation $\"\"$ .

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$\"\"$

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Apply the definition of logarithm is : $\"\"$ if and only if $\"\"$ .

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$\"\"$ .

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Apply power $\"\"$ on each side.

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$\"\"$

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Apply the definition of logarithm is : $\"\"$ if and only if $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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Power property of logarithm is proved.

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$\"\"$

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The power property of logarithm $\"\"$ .