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Logarithmic Scales

Page history last edited by PBworks 16 years, 7 months ago






 A logarithmic graph is the inverse of an exponential graph. this is because exponential graphs are written as Formula whereas logarithmic graphs are written as Formula   or   Formula when graphed, they look like this:


Logarithmic equations can be graphed on a logarithmic scale in order to create a linear graph. This means that the Y value, insead of going up by the same value for equal spaces, will go up by the same value to an exponent, with the exponent values equally spaced.It looks like this:


Logarithmic scales are used to measure, among other things, earthquake magnitude (richter scale) and sound levels (decebels)


Richter Scale for measuring earthquake magnitude:                              Decebel level for measuring sound:


 Formula                                                                                Formula


R = Richter value                                                                                     D = sound in Decebels (dB)


I = intensity (amplitude of largest wave on seismograph in microns)     I = sound intensity Formula


Formula= reference intensity (1)                                                                 Formula=reference sound Formula





a Problem:


Imagine yourself as a very thrifty man with a great concern for saftey. You are looking to buy a home and have narrowed your choices down to two.

The white home can withstand an earthquake of up to 5.6 on the Richter Scale, the not-white home can withstand an earthquake of up to 6.2 on the Richter scale. If the not-white home costs 4 times as much as the white one, which will give you the most bang resistance for your buck?


Here's your Answer:


Richter value - white home = 5.6                                                                                                          Richter value-not-white home = 6.2



Formula                                                                                          Formula        


 Formula                                                                                                     Formula


Formula                                                                                         Formula





Though it is very close, the not-white house is not as many times as quake resistant (3.98) as it is expensive (4).Therefore, the white house would be a better buy.


Graphs taken from http://graphicsserver.com/com_products/images/GraphChoiceLog1.gif and http://home.alltel.net/okrebs/Ch5-22.gif

Comments (1)

Anonymous said

at 10:06 pm on Apr 29, 2007

Nice job Lena. Your LaTex formulas look great. A very well done and challenging sample problem.

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