Exponential and Logarithmic Functions

Question

Determine the intensity of the sound of an audience applauding, if the sound level is 150dB. 

Loudness formula L= 10log(i/i0), i= intensity, i0=1

Answer 1

Hello Stephen,

I think you might be missing numbers for i0 which typically equals 10^-12.

You know L = 150 dB and i0, so you're solving for i:

150 = 10 log(i/10^-12).

Divide both sides by 10: 15 = log(i/10^-12)

From there: you can convert this log equation into an exponential equation: 10¹⁵ = i/10^-12

Multiply both sides by 10^-12: 10¹⁵ x 10^-12 = i; therefore i = 10³ = 1000

Answer: i = 1000