4 3 Properties Of Logarithms
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Section 4.3 Properties of Logarithms
Transcript of 4 3 Properties Of Logarithms
Section 4.3Properties of Logarithms
The Product Rule
Example
3
Use the product rule to expand each logarithmic expression.
log (9 5)
log (1000x)
⋅
The Quotient Rule
Example
5
3
Use the quotient rule to expand each logarithmic expression.
25log
log8
ln7
x
x
e
The Power Rule
2:
When we use the power rule to "pull the exponent to the front"
we say that we are expanding a logarithmic expression. For example
we can use the power rule to expand ln x
Example
25
42
5
Use the power rule to expand each logarithmic expression.
log 7
log (8 )
log
ln(6 )
x
x
e
Expanding Logarithmic Expressions
Study Tip
Example
( )
( )
2
3
5
Use logarithmic properties to expand each expression as
much as possible.
log
25log
10ln
log 9 10
b x z
y
e
Condensing Logarithmic Expressions
Example
( )
( )
2 2
3 3
Write as a single logarithm (condense).
log 4 log 8
log 6 log 6
2 log 9 log 27
ln 2 5ln
x
x x
+−
−− +
The Change-of-Base Property
Graphing Calculator
Example
4Use common logarithms to evaluate log 12.
Use your calculator.
(a)
(b)
(c)
(d)
9
Use properties of logarithms to expand each expression.
Where possible, evaluate without a calculator.
81log
x
9
9
2
2 log
2
log
2
x
x
x
x
−−
(a)
(b)
(c)
(d)
3
Use properties of logarithms to expand each expression.
Where possible, evaluate without a calculator.
log 27y
3
3
3
3
3log
log 3 log
log 3 log
1 log
y
y
y
y
−
+
+
