 ## CCSS.MATH.CONTENT.HSF.LE.A.4

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### In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of logarithmic functions. Such disparate phenomena as hearing loss and tsunamis can be explained through logarithmic models. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-logarithmic-functions ### The mathematical definition of a logarithm is the inverse of an exponential function, but why do we need to use logarithms? This segment explains the nature of some data sets, where incremental changes in the domain result in explosive changes in the range. As a result, logarithms allow for the a way to present and analyze what would otherwise be unwieldy data. This video includes a video transcript: https://www.media4math.com/library/video-transcript-algebra-applications-logarithmic-functions-segment-1-what-are-logarithms ### We live in a noisy world. In fact, prolonged exposure to noise can cause hearing loss. Students analyze the noise level at a rock concert and determine the ideal distance where the noise level is out of the harmful range. Using the TI-Nspire’s Geometry tools, student create a mathematical simulation of the decibel level as a function of distance. This video includes a video transcript: https://www.media4math.com/library/video-transcript-algebra-applications-logarithmic-functions-segment-2-hearing-loss A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-hearing-loss ### In 1998 a devastating tsunami was triggered by a 7.0 magnitude earthquake off the coast of New Guinea. The amount of energy from this earthquake was equivalent to a thermonuclear explosion. Students analyze the energy outputs for different magnitude earthquakes. Using the Graphing tools, students explore the use of a logarithmic scale to better analyze exponential data. This video includes a video transcript: https://www.media4math.com/library/video-transcript-algebra-applications-logarithmic-functions-segment-3-tsunamis A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-tsunamis ### This video begins with the historical invention of logarithms that forever changed the world of computation—until the advent of calculators more than 300 years later. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it proceeds to derive the properties of logs, examine logarithmic functions and graphs, and finally explore the well-known Richter logarithmic scale. Concepts explored: functions and inverse functions, logarithms, exponential functions, logarithmic functions. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-nspirations-logarithms-and-logarithmic-functions A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-nspirations-logarithmic-functions ### In this Investigation we look at properties of logarithms. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Logarithms and Logarithmic Functions. Segments 1 and 2 are grouped together. To access Algebra Nspirations: Logarithms and Logarithmic Functions, Segment 2, click the following link: • https://www.media4math.com/library/algebra-nspirations-logarithms-and-logarithmic-functions-segment-2 A Video Transcript for Algebra Nspirations: Logarithms and Logarithmic Functions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-logarithms-and-logarithmic-functions-part-1 ### In this Math Lab we look at patterns among different logarithm calculations. This video is Segment 2 of a 4 segment series related to Algebra Nspirations: Logarithms and Logarithmic Functions. Segments 1 and 2 are grouped together. To access Algebra Nspirations: Logarithms and Logarithmic Functions, Segment 1, click the following link: • https://www.media4math.com/library/algebra-nspirations-logarithms-and-logarithmic-functions-segment-1 A Video Transcript for Algebra Nspirations: Logarithms and Logarithmic Functions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-logarithms-and-logarithmic-functions-part-1 ### In this Investigation we look at logarithmic functions and graphs. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Logarithms and Logarithmic Functions. Segments 3 and 4 are grouped together. To access Algebra Nspirations: Logarithms and Logarithmic Functions, Segment 4, click the following link: • https://www.media4math.com/library/algebra-nspirations-logarithms-and-logarithmic-functions-segment-4 A Video Transcript for Algebra Nspirations: Logarithms and Logarithmic Functions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-logarithms-and-logarithmic-functions-part-2 ### In this Math Lab we look at an application of logarithms involving astronomy. This video is Segment 4 of a 4 segment series related to Algebra Nspirations: Logarithms and Logarithmic Functions. Segments 3 and 4 are grouped together. To access Algebra Nspirations: Logarithms and Logarithmic Functions, Segment 3, click the following link: • https://www.media4math.com/library/algebra-nspirations-logarithms-and-logarithmic-functions-segment-3 A Video Transcript for Algebra Nspirations: Logarithms and Logarithmic Functions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-logarithms-and-logarithmic-functions-part-2 ### The definition of the term "Graphs of Exponential Functions." ### Math Clip Art--Logarithmic Function. An illustration of a logarithmic function graph. Note: The download is a JPG file. ### Example 1: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, c = 1. ### Example 2: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, c > 1. ### Example 3: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, c < 0. ### Example 4: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, 0< c < 1. ### Example 5: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a > 0, c = 1. ### Example 6: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a < 0, c = 1. ### Example 7: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a > 0, c > 1. ### Example 8: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a < 0, c > 1. ### Example 9: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a > 0, 0 < c < 1. ### Example 10: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, 0 < c < 1. ### Example 11: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: b = 2, a = 1, c = 1. ### Example 12: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: b = 2, a = 1, c > 1. ### Example 13: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: b = 2, a = 1, c < 0. ### Example 14: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: b = 2, a = 1, 0< c < 1. 