Intensity Increase for 30dB & 22dB: Log Homework Solved

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To determine the intensity increase for sound levels of 30dB and 22dB, the formula I = I0 * 10^(β/10) is used, where I0 is the reference intensity (1x10^-12 W/m²). For a 30dB increase, the intensity becomes 1000 times greater than the reference level, while a 22dB increase results in approximately 158 times the reference intensity. The challenge lies in manipulating the logarithmic equation to isolate I. Understanding how to apply logarithmic properties is crucial for solving these types of problems. Mastering these calculations is essential for effective use of hearing aids.
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Homework Statement



A hearing aid increases the sound intensity level, thereby allowing a person to hear better. For the following decibel increases, by how much does the intensity of sound increase?

a)30dB
b) 22dB

Homework Equations



\beta=10log (I/Io)

The Attempt at a Solution


I substitute 30 in for the beta, and 1x10^-12 for the Io, but i can't seem to solve for the correct answer. Can anyone lend a hand?

I really have trouble with bringng to log to the other side. Thanks
 
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\frac{\beta}{10} = \log_{10} (I/I_0)

By the definition of the logarithm, I/I_0 = 10^{\frac{\beta}{10}}

So I = I_0 \cdot 10^{\frac{\beta}{10}}
 

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