{"id":15975,"date":"2019-12-05T05:17:10","date_gmt":"2019-12-05T05:17:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/introduction-logarithms-and-logarithmic-functions\/"},"modified":"2019-12-05T05:17:31","modified_gmt":"2019-12-05T05:17:31","slug":"introduction-logarithms-and-logarithmic-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/introduction-logarithms-and-logarithmic-functions\/","title":{"raw":"Introduction to Logarithmic Functions","rendered":"Introduction to Logarithmic Functions"},"content":{"raw":"\n
\n\n[caption id=\"\" align=\"aligncenter\" width=\"488\"]\"Photo Devastation of the earthquake which happened on March 11, 2011 in Honshu, Japan. (credit: Daniel Pierce)[\/caption]<\/figure>\n

In [latex]2010[\/latex], a major earthquake struck Haiti, destroying or damaging over [latex]285,000[\/latex] homes.[footnote]http:\/\/earthquake.usgs.gov\/earthquakes\/eqinthenews\/2010\/us2010rja6\/#summary<\/a>. Accessed [latex]3\/4\/2013[\/latex].[\/footnote] One year later, another, stronger earthquake devastated Honshu, Japan, destroying or damaging over [latex]332,000[\/latex] buildings,[footnote]http:\/\/earthquake.usgs.gov\/earthquakes\/eqinthenews\/2011\/usc0001xgp\/#summary<\/a>. Accessed [latex]3\/4\/2013[\/latex].[\/footnote] like those shown in the picture above. Even though both caused substantial damage, the earthquake in [latex]2011[\/latex] was [latex]100[\/latex] 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 [latex]7.0[\/latex] on the Richter Scale[footnote]http:\/\/earthquake.usgs.gov\/earthquakes\/eqinthenews\/2010\/us2010rja6\/<\/a>. Accessed [latex]3\/4\/2013[\/latex].[\/footnote] whereas the Japanese earthquake registered a [latex]9.0[\/latex].[footnote]http:\/\/earthquake.usgs.gov\/earthquakes\/eqinthenews\/2011\/usc0001xgp\/#details<\/a>. Accessed [latex]3\/4\/2013[\/latex].[\/footnote]<\/p>\n

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 [latex]4[\/latex]. It is [latex]{10}^{8 - 4}={10}^{4}=10,000[\/latex] times as great! In this lesson, we will investigate the nature of the Richter Scale and the base-ten function upon which it depends.<\/p>\n","rendered":"

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\"Photo<\/p>\n

Devastation of the earthquake which happened on March 11, 2011 in Honshu, Japan. (credit: Daniel Pierce)<\/p>\n<\/div>\n<\/figure>\n

In [latex]2010[\/latex], a major earthquake struck Haiti, destroying or damaging over [latex]285,000[\/latex] homes.[1]<\/sup><\/a> One year later, another, stronger earthquake devastated Honshu, Japan, destroying or damaging over [latex]332,000[\/latex] buildings,[2]<\/sup><\/a> like those shown in the picture above. Even though both caused substantial damage, the earthquake in [latex]2011[\/latex] was [latex]100[\/latex] 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 [latex]7.0[\/latex] on the Richter Scale[3]<\/sup><\/a> whereas the Japanese earthquake registered a [latex]9.0[\/latex].[4]<\/sup><\/a><\/p>\n

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 [latex]4[\/latex]. It is [latex]{10}^{8 - 4}={10}^{4}=10,000[\/latex] times as great! In this lesson, we will investigate the nature of the Richter Scale and the base-ten function upon which it depends.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Original<\/div>