Rock Concert vs Whisper: Intensity Factor of 22026.4

[roam]

Homework Statement

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively?

Homework Equations

The sound level of a sound wave in decibles is

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

Also the ratio of intensities:

$$\beta_B - \beta_A = 10 log (\frac{I_B}{I_A})$$

The Attempt at a Solution

Using the latter equation:

$$100 = 10 log (\frac{I_B}{I_A})$$

Solving for the ratio I get 22026.4. Now how can I determine the factor one intensity is greater than the other? I'm not quite sure...

 

[rl.bhat]

Homework Statement

$$\beta_B - \beta_A = 10 log (\frac{I_B}{I_A})$$

The Attempt at a Solution

Using the latter equation:

$$100 = 10 log (\frac{I_B}{I_A})$$

Solving for the ratio I get 22026.4. Now how can I determine the factor one intensity is greater than the other? I'm not quite sure...

The equation should be

$$100 = 10log_{10}(\frac{I_A}{I_B})$$

Or $$10 = log_{10}(\frac{I_A}{I_B})$$

Now find the ratio of the intensities.