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Logarithmic Scales

last edited by 16 years, 7 months ago

Lena

Explaination:

A logarithmic graph is the inverse of an exponential graph. this is because exponential graphs are written as whereas logarithmic graphs are written as    or   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:

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

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

= reference intensity (1)                                                                 =reference sound

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?

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

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