An equation for loudness l in decibels is given by l= 10logr where r is the sound’s relative intensity. an air-raid siren can reach 150 decibels and jet engine noise can reach 120 decibels. how many times greater is the relative intensity of the air-raid siren than that of the jet engine noise?

We are asked to find ratio of two relative intensities. Let's start by rearranging formula for R:


For air-raid siren we have:

For jet engine noise we have:


To find out many times greater is the relative intensity of the air-raid siren than that of the jet engine noise we need to divide these two numbers:
tex] \frac{R_{1}}{R_{2}} = \frac{10^{15}}{10^{12}} =10^{3}=1000[/tex]

7.666270253x10 raised to the 18th power