A listener triples his distance from a source that emits sound uniformly in all directions. by how many decibels does the sound intensity level change?

Sound intensity goes inversely as the square of the distance from the source. This is easy to understand if you think of the total sound energy spread out over the surface of a sphere with the source at the center. The surface area of the sphere goes as r^2, so the power density goes inversely as such.

The decibel change is simply

Change = 10 log10 ((1/3) ^2) = - 9.54 dB