Logarithm Word Problems

Logarithm Word Problems - Grade 10

Read each word problem carefully and use your knowledge of logarithms to solve them. Show all your work.

1. The population of a certain bacteria doubles every 30 minutes. If there are initially 100 bacteria, how long will it take for the population to reach 10,000?

2. A radioactive substance decays at a rate of 5% per hour. If you start with 500 grams of the substance, how long will it take until only 100 grams remain?

3. The Richter scale measures the magnitude of an earthquake. An earthquake with magnitude 7 is 10 times more powerful than an earthquake with magnitude 6. How many times more powerful is an earthquake with a magnitude of 8 compared to an earthquake with a magnitude of 5?

4. If you invest $1000 at an annual interest rate of 6% compounded continuously, it will take approximately   years for your investment to double. (Use the formula A = Pe^(rt))

5. The loudness of a sound is measured in decibels (dB). A sound that is 10 times more intense than another sound is 10 dB louder. If a rock concert produces a sound intensity that is 1,000,000 times greater than a normal conversation, what is the difference in decibels?