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Try It 10.51: Calculating the Decibel Level of a Dishwasher

To determine the decibel level of a quiet dishwasher with an intensity of 10710^{-7} watts per square inch, use the decibel level formula D = 10 \log\left(\frac{I}{10^{-12}} ight). Substituting the given intensity, II, into the formula yields D = 10 \log\left(\frac{10^{-7}}{10^{-12}} ight). Simplifying the expression inside the logarithm gives D=10log(105)D = 10 \log(10^5). Since log105=5\log 10^5 = 5, the decibel level evaluates to D=105D = 10 \cdot 5, which equals 5050 dB.

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Updated 2026-05-25

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