Reducing the intensity of noise by a factor of 10 will mean a reduction in the noise level by

The decibel scale measures noise level as ten times the logarithm of the intensity ratio.

Cutting intensity by a factor of ten gives the logarithm of one tenth, which is minus one.

Multiplying that by ten yields a fall of ten decibels in the noise level.

A twenty decibel drop would need intensity cut by a factor of one hundred, not ten.

Falls of three or six decibels correspond to halving or quartering, smaller changes than tenfold.

Because the scale is logarithmic, equal decibel steps mean equal multiplying factors of intensity.