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Study Guides > Intermediate Algebra

Introduction: Logarithmic Functions

Photo of the aftermath of the earthquake in Japan with a focus on the Japanese flag. Figure 1. Devastation of March 11, 2011 earthquake in Honshu, Japan. (credit: Daniel Pierce)

In 20102010, a major earthquake struck Haiti, destroying or damaging over 285,000285,000 homes.[footnote]http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010rja6/#summary. Accessed 3/4/20133/4/2013.[/footnote] One year later, another, stronger earthquake devastated Honshu, Japan, destroying or damaging over 332,000332,000 buildings,[footnote]http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/#summary. Accessed 3/4/20133/4/2013.[/footnote] like those shown in the picture above. Even though both caused substantial damage, the earthquake in 20112011 was 100100 times stronger than the earthquake in Haiti. How do we know? The magnitudes of earthquakes are measured on a scale known as the Richter Scale. The Haitian earthquake registered a 7.07.0 on the Richter Scale[footnote]http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010rja6/. Accessed 3/4/20133/4/2013.[/footnote] whereas the Japanese earthquake registered a 9.09.0.[footnote]http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/#details. Accessed 3/4/20133/4/2013.[/footnote]

The Richter Scale is a base-ten logarithmic scale. In other words, an earthquake of magnitude 8 is not twice as great as an earthquake of magnitude 44. It is 1084=104=10,000{10}^{8 - 4}={10}^{4}=10,000 times as great! In this lesson, we will investigate the nature of the Richter Scale and the base-ten function upon which it depends.

The learning objectives for this lesson include:

  • Convert from logarithmic to exponential form
  • Convert from exponential to logarithmic form
  • Evaluate logarithms
  • Use common logarithms
  • Use natural logarithms

The learning activities for this lesson include:

  • Read: Composite and Inverse Functions
  • Self-Check: Composite and Inverse Functions
  • Read: Define Logarithmic Functions
  • Self-Check: Define Logarithmic Functions
  • Read: Evaluate Logarithms
  • Self-Check:Evaluate Logarithms
  • Read: Graphs of Logarithmic Functions
  • Self-Check: Graphs of Logarithmic Functions

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