$\"\"$

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Find intensity of auditorium when the level of sound is $\"\"$ .

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The equation of level of sound is $\"\"$ , where $\"\"$ is an intesity of $\"\"$ .

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

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$\"\"$

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

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$\"\"$

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

\

$\"\"$

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

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$\"\"$

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$\"\"$

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

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$\"\"$ .

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Intensity of auditorium when the level of sound $\"\"$ is $\"\"$ .

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$\"\"$

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Find intensity of auditorium when the level of sound is $\"\"$ .

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

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$\"\"$

\

$\"\"$

\

$\"\"$

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$\"\"$

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$\"\"$

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Intensity of auditorium when the level of sound $\"\"$ is $\"\"$ .

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The percentage of decrease in the intensity : $\"\"$ .

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$\"\"$

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Therefore, the percentage of decrease in the noise due to the material is $\"\"$ .

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$\"\"$

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The percentage of decrease in the noise due to the material is $\"\"$ .