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If the intensity increased by a factor o...

If the intensity increased by a factor of 20, by how may decibels is the sound level increased?

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Let the initial intensity be I and te sound level be `beta_1`. When the intensity is increased to 20 I, the level increases to `beta_2`.
`Then beta_1=10log(I/I_0)`
and `beta_2=10log(20I/I)`
`Thus, beta_2-beta_1=10log(20I/I)`
`=10log 20`
`=13dB`.
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