# lec4 - Log relationships trig functions earthquakes...

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1 Log relationships, trig functions, earthquakes & computer lab tom.h.wilson [email protected] Department of Geology and Geography West Virginia University Morgantown, WV Logarithms The allometric or exponential functions are in the form cx ab y and cx a y 10 b and 10 are the bases. These are constants and we can define any other number in terms of these constants raised to a certain power. x y e i 10 . . Given any number y, we can express y as 10 raised to some power x Thus, given y =100, we know that x must be equal to 2.

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2 x y 10 By definition, we also say that x is the log of y, and can write   x y x 10 log log So the powers of the base are logs. “log” can be thought of as an operator like x (multiplication) and which yields a certain result. Unless otherwise noted, the operator “log” is assumed to represent log base 10 . So when asked what is 4 y wher lo 45 y where , log y We assume that we are asking for x such that 45 10 x Sometimes you will see specific reference to the base and the question is written as 45 y where , log 10 y y 10 log leaves no room for doubt that we are specifically interested in the log for a base of 10.
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lec4 - Log relationships trig functions earthquakes...

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