By what factor must the sound intensity be increased to increase the sound intensity level by 13.8 db?

Increasing the sound intensity by a factor of:

10 raises its level by 10 dB

100 raises its level by 20 dB

1,000 raises its level by 30 dB

10,000 raises its level by 40 dB

therefore, we would be using the 10dB since we are only looking for 13.8 dbSo: 10^1.38 = 23.99 or 24 times.