Math 1310
Section 5.3
Logarithms
Earlier, you learned to find the inverse of a function.
Let’s apply the same method from
Chapter 3 to help find the inverse of an exponential function.
If
x
x
f
3
)
(
=
, rewrite the function as
x
y
3
=
.
Interchange
x
and
y
:
y
x
3
=
.
Now we need to solve the equation for
y
.
Hmmmmm.
We need something to help us out here.
We want to be able to choose values for the
independent variable,
x
, and then easily calculate
y
and from this form of the equation,
there is no such easy calculation.
Enter logarithms.
For
1
,
0
≠
a
a
, the logarithm with base
a
, written
x
a
log
is the exponent to which
a
must be raised in order to give
x
.
There are two very special logs:
The
common logarithm
is the logarithm with base 10.
We denote this as
x
x
log
log
10
=
.
The
natural logarithm
is the logarithm with base
e
.
We denote this as
x
x
e
ln
log
=
You will find both of these logarithms on a scientific calculator.
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 Summer '08
 MARKS
 Exponential Function, Natural logarithm, Logarithm

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