## Tuesday, February 8, 2011

### Practical logarithmic problems

There was a 7.6 earthquake in Mindanao in the Philippines and a 5.7 aftershock three days later. Rounded to the nearest multiple of 10, how much stronger was the bigger quake?

One singer is measured at 64 dB. Eight singers at the same level would have eight times more energy. To the nearest decibel, what is the decibel level of the eight singer chorus?

Prof. Hubbard said...
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Prof. Hubbard said...

There was a 7.6 earthquake in Mindanao in the Philippines and a 5.7 aftershock three days later. Rounded to the nearest multiple of 10, how much stronger was the bigger quake?

Answer: 7.6 - 5.7 = 1.9, then we multiply by 1.5 to get 2.85 and 10^2.85 = 707.9457...; since the answer is to be rounded to two significant digits, the first quake was 710 times stronger than the aftershock.

One singer is measured at 64 dB. Eight singers at the same level would have eight times more energy. To the nearest decibel, what is the decibel level of the eight singer chorus?

Answer: log 8 = .903089987, which would round to .9 bels or 9 decibels. 64 + 9 = 73, so the chorus of eight singers would give a reading of 73 db.