A sound's noise level is measured in decibels (dB) by comparing the sound's intensity, $I$, to a benchmark sound that has an intensity of $10^{-16}$ watts/cm$^2$. In particular, $$\text{dB}=10\log(I/10^{-16})=10\log(10^{16}I).$$

A single jet engine that is 100 feet away from the listener has a noise level of 140dB.

a) Find the sound intensity of the jet engine in watts/cm$^2$.
watts/cm$^2$

b) Suppose two jet engines are 100 feet away from a person, each with the same sound intensity as the jet engine from part (a). What is the combined noise level in decibels? [Hint: the combined sound intensity is the sum of the intensities of the two engines.]
dB

c) Suppose a source has sound intensity $I$. Using the definition of decibels, write an expression for the noise level in decibels if two sources with sound intensity $I$ are present.
$D(I) =$

d) Using properties of logarithms, write the expression from part (c) as the sum of two logarithms.
$D(I) =$

Hint: