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Math 1310
Section 5.4
Properties of Logarithms
•
You will sometimes be asked to rewrite logarithmic expressions in either an
expanded or contracted form.
•
To do this, you will use the Laws of Logarithms.
•
You must know all 8 of the Laws of Logarithms.
Laws of Logarithms
If
m
,
n
and
b
are positive numbers,
1
≠
b
, then
1.
n
m
mn
b
b
b
log
log
log
+
=
2.
n
m
n
m
b
b
b
log
log
log

=
3.
m
n
m
b
n
b
log
log
=
4.
0
1
log
=
b
5.
1
log
=
b
b
6.
x
b
x
b
=
log
7.
x
b
x
b
=
log
8.
b
m
m
b
log
log
log
=
(change of bases formula)
These properties are true for logs of any base, including common logs and natural logs.
Example 1:
Rewrite each of the following expressions in a form that has no logarithms
of a product, quotient or power.
a.
x
5
log
3
b.
( 29
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This note was uploaded on 02/22/2012 for the course MATH 1310 taught by Professor Marks during the Summer '08 term at University of Houston.
 Summer '08
 MARKS
 Math

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