Mathematics 30-1 Module 6

Read through “Example 4” on page 377 of the textbook. How does the strategy used in “Example 4” to estimate the value of log2 14 compare with the strategy you used in Try This 4?

Self-Check 3

Estimate the value of log3 30 to one decimal place. Explain your answer. Answer

This is an image of a seismograph machine. There is a needle that moves back and forth on grid paper to indicate the amplitude of seismic waves.

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Logarithms are helpful in different science applications where logarithmic scales are used. In this activity you will explore the Richter scale, which is a logarithmic scale.

Earthquakes produce seismic waves that are recorded on seismographs. The magnitude of an earthquake is determined from the logarithm of the amplitude of the waves recorded on the seismograph. The Richter scale is used to measure the magnitude of an earthquake. Each whole-number increase in magnitude represents an increase of ten times in measured amplitude of the seismic wave.

Try This 5

The relationship between the amplitude of an earthquake and the Richter scale is defined as , where

M is the magnitude on the Richter scale
A is the amplitude of the earthquake
A0 is the amplitude of a standard earthquake

Near the east coast of Honshu, Japan, on March 11, 2011, there was a very large earthquake with magnitude 9.0 on the Richter scale. On April 7, 2011, there was an aftershock from the earlier earthquake with magnitude 7.1 on the Richter scale.

For the initial earthquake, determine how many times greater the amplitude of the earthquake was compared to a standard earthquake, A0.
Determine how many times greater the amplitude of the seismic wave of the 9.0-magnitude earthquake was compared to the amplitude of the 7.1-magnitude earthquake.

Save your responses in your course folder.

Did You Know?

This is a photo of a damaged building.

iStockphoto/Thinkstock

The Richter scale was created by American Seismologist Charles F. Richter in 1935. The scale measures the shaking of the ground 100 km from the quake’s epicenter. The Richter scale is a logarithmic scale. So, for each whole-number increase on the scale, the magnitude is increased ten-fold. For example, an earthquake that measures 1.0 on the Richter scale will not even be felt by humans, but a quake that registers 4.0 will cause buildings to shake.

An earthquake that registers 8.0 or higher can be catastrophic. The most powerful earthquake ever recorded occurred in Chile in 1960. This quake had a magnitude of 9.5 on the Richter scale. The 2011 earthquake in Japan registered 9.0 on the Richter scale. This earthquake and the resulting tsunami caused incredible damage and loss of life.

This is a graph of the ground motion of an earthquake as a function of the magnitude of an earthquake on the Richter scale. As the ground motion increases, the magnitude of the earthquake increases.

Module 6: Exponents and Logarithms

Self-Check 3

Try This 5