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Source: College Mathematics
, Rockswold G., Bennett J., and Briggs W.
C:/CLASES_COLEGIO/2007/NOTAS/0102/
02/13/07
Math 1332  College Mathematics
Chapter 54 Notes
Logarithmic Functions and Models
We learned how to solve linear and quadratic equations, we now solve for exponential equations of
the form
a = k
x
, where the variable
x
is an exponent.
We introduce logarithmic functions, which
model data that grows much at a slower pace than exponential functions.
Logarithmic functions
can be used to solve exponential equations.
Base
a
Logarithms
Logarithm
:
The logarithm with base
a
of a positive number
x
, is defined as
log
a
x = k
if and only if
x = a
k
,
where
a > 0, a
≠
1,
and
k
is a real number.
f(x) = log
a
x
Æ
is the
Logarithmic Function with base
a
Note
Æ
A logarithm is an exponent (
k
)
Inverse Properties of Logarithm
:
•
log
a
a
x
= x
for a any real number
x
•
a
log a x
= x
for any positive number x
Ex:
log
3
9
log
¼
64
Graph of
y =
log
a
x
Æ
•
always passes through the point (1,0) since
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 Fall '11
 MariselaA.Martinez
 Equations, Logarithmic Functions

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