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(All Steps) The loudness of sound (L, measured in decibels) perceived by the human ear depends on intensity levels (I) according to L=10log_10((I)/(I_0)),

Question: The loudness of sound (L, measured in decibels) perceived by the human ear depends on intensity levels (I) according to \(L=10{{\log }_{10}}\left( \frac{I}{{{I}_{0}}} \right)\), where Io is the standard threshold of audibility. If x=I/Io then using the change-of-base formula, we get \(L=\frac{10\ln x}{\ln 10}\). At what rate is the loudness changing with respect to x when the intensity is 50 times the standard threshold of audibility (that is, when x = 50)?

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