# Intensity : Log

1. Nov 20, 2007

### carmenn

1. The problem statement, all variables and given/known data

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

2. Relevant equations

$$\beta=10log (I/Io)$$

3. 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

2. Nov 21, 2007

### Gib Z

$$\frac{\beta}{10} = \log_{10} (I/I_0)$$

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

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