THe loudness L of a sound is measured by L=10 log10^R where R is the sound's relative intensity. One person talks with a relative intensity of 10^6 or 60 decibels. How much louder would 100 people be ,talking with the same intensity.

Question

So would I just use L= 10log10^1/10^6? and then multiply by 100 when done. I am supposed to use the Quotient property of logarithms.

Answer 1

I1 = 10^6.

I2 = 10^2*10^6 = 10^8.

db(increase) = 10*Log(I2/I1).
db(increase) = 10*Log(10^8/10^6) = 20.