Approximately how many times louder is the latter sound?

Question

The sound level measured in a room by a person watching a movie on a home theater system varies from 40 dB during a quiet part to 80 dB during a loud part. Approximately how many times louder is the latter sound?

Answer 1

Using the decibel definition, 40 dB = 10 log₁₀ (I₁ /I_o), log₁₀ (I₁ /I_o) = 4, I₁ = 10⁴ I_o.

Meanwhile 80 dB = 10 log₁₀ (I₂ /I_o), log₁₀ (I₂ /I_o) = 8, I₂ = 10⁸ I_o. So I₂ is 10,000 times louder than I₁.