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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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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 Spring '09
 Geography, Geology, Logarithm, Department of Geology and Geography

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