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IB Precalculus
Unit 3: Logarithms and Exponents
Applications of Logarithms
1. The most intense recorded earthquake in the state of New York occurred in 1944; it had Richter
magnitude 5.8. The most intense recorded earthquake in Minnesota occurred in 1975; it had
Richter magnitude 5.0. Approximately how many times more intense was the 1944 earthquake in
New York than the 1975 earthquake in Minnesota.
2. The most intense recorded earthquake in Texas occurred in 1931; it had Richter magnitude 5.8.
If an earthquake were to strike Texas next year that was three times more intense than the
current record in Texas, what would its Richter magnitude be?
3. Suppose you whisper at 20 decibels and normally speak at 60 decibels?
(a) What is the ratio of the sound intensity of your normal speech to the sound intensity of your
whisper?
(b) How many times louder does your normal speech seem as compared to your whisper?
4. Suppose your cell phone rings with a noise of 74 decibels, and you normally speak at 61 decibels.
(a) What is the ratio of the sound intensity of your cell phone ring to the sound intensity of your
normal speech?
(b) How many times louder does your cell phone ring seem than your normal speech?
5. Sirius, the brightest star that can be seen from Earth (not counting the sun), has an apparent
magnitude of -1.4. Vega, which was the North Star about 12,000 years ago (slight changes in the
Earth’s orbit lead to changing North Stars every several thousand years), has an apparent
magnitude of 0.03. How many times brighter than Vega is Sirius?
6. The full moon has an apparent magnitude of approximately -12.6. How many times brighter
than Sirius is the full moon?
7. Neptune has an apparent magnitude of about 7.8. What is the apparent magnitude of a star that
is 20 times brighter than Neptune?