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# Logarithmic question using decibels?

Restaurant conversation is about 45 dB. If ordinary conversation is 100 times greater than restaurant conversation, how loud is ordinary conversation?

Using the formula: L = 10log (I/I0) for decibels.

Could someone show me step by step how to solve this so I can learn how? Thank you!

### 1 Answer

- chauncyLv 74 years agoFavorite Answer
L = 10 log (I/Io)

where L = loudness, I = intensity and Io is a reference intensity level.

Let the intensity of restaurant conversation = Ir and of ordinary conversation = Ioc

45 = 10 log (Ir/Io)

log (Ir/Io) = 4.5

Ir/Io = 10^4.5

Ir = Io * 10^4.5

Ioc = 100 * Io * 10^4.5 = Io * 10^6.5

Ioc/Io = 10^6.5

The loudness of ordinary conversation = 10 log (Ioc/Io)

= 10 log (10^6.5)

= 10 * 6.5

= 65

Note: The letters o, r and oc are subscripts.

Io is the intensity when L = 0.

If I = Io then L = 10 log (Io/Io) = 10 log 1 = 10 * 0 = 0

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