1
Summer MA 15200
Lesson 22
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
:
mn
bb 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
bb
b
M
NM
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
bx
y
ca
b
de
=
=
=
=
II
Quotient Rule
Quotient Rule for Exponents
:
m
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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