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

[carmenn]

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

 

[Gib Z]

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

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

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