3.3 properties of logarithms 2015. hwq copyright © by houghton mifflin company, inc. all rights...
TRANSCRIPT
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3.3 Properties of Logarithms
2015
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HWQ
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32 log 3f x x
Find the Domain, Vertical Asymptote, and x-intercept. Sketch a graph:
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Change of base Formula
1) log4 25
2) log2 12
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loglog
loga
xx
a
= 2.3219
= 3.5850
To change the base, take the log of the tall over the log of the small.
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1. If then
2.
3.
4.
5.
6.
Properties of Logarithms
y xblog b xy
loga 1 0
log ( ) log logb b buv u v
log log logb b b
u
vu v
log logbx
bu x u
logaxa x
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Use properties of logarithms to expand each expression:
1)
2)
3)
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5log (5 )x
8
1log
4
72log x
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Solve for x.a. b.
Simplify.
c.
log log2 2 3x 4
1log
64x
25log 5
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Example: Use the product property to verify: log ( ) log logb b buv u v
2 2 2log 32 log 8 log 4
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Use the properties of logarithms to rewrite and simplify the logarithmic expression.
Example
2 42log 4 8
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Use the properties of logarithms to expand each expression:
a. b.
Example
log435x y ln
3 5
7
x
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Use the properties of logarithms to expand:
Example
4
4logb
x y
z
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Use the properties of logarithms to condense
(write as a single log):
Examples
1
23 110 10log log ( )x x
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Use the properties of logarithms to condense
(write as a single log):
Examples
1
342 2log log ( )x x
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Use the properties of logarithms to condense
(write as a single log):
Examples
2ln 3ln 4ln 5ln 6ln 2ln 8ln 5lnx x y x y z z d
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Use the properties of logarithms to condense
(write as a single log):
Examples
log 2log 3logcb b bc b z c bc
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Use the properties of logarithms to condense
(write as a single log):
Examples
2 3 2log 1 log 1 log 1 log 1 log 1x x x x x x
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Day 1: Pg. 203: 9-41 odd, 45-61 odd, 67, 79
Day 2: Properties of logs WS
And optional: pg. 239 #32-36, 41-44, and 69-76.
Homework
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HWQ 9/19
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1log log 5
3x x
Condense the expression to the logarithm of a single quantity: