1
MA 15200
Lesson 29
Section 4.3
This lesson is on the
properties of logarithms.
Properties of logarithms model the
properties of exponents.
I
Product Rule
Product Rule of Exponents
:
m n
m n
b b
b
Notice:
When the bases were the same, the
exponents were added
when multiplication
was performed.
Likewise
logarithms are added
when multiplication is performed in the
argument.
Product Rule of Logarithms
:
log (
)
log
log
b
b
b
MN
M
N
In words, the logarithm of a product is the sum of the logarithms.
When a single logarithm is written using this product rule,
we say we are
expanding the logarithmic expression.
Ex 1: Assume all variables represent positive values.
Use the product rule to expand each expression
and simplify where possible.
2
2
5
)
log (7 )
)
log
2
)
log(100
)
)
ln(20 )
b
ar
b
x y
c
ab
de
II
Quotient Rule
Quotient Rule for Exponents
:
m
mn
n
b
b
b
Notice:
When the bases were the same, the
exponents were subtracted
when division
was performed.
Likewise,
logarithms are subtracted
when division is performed in the
argument.
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 Fall '09
 Exponents, Derivative, Product Rule, Natural logarithm, Logarithm

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