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3.3 Properties of Logarithms
2015
HWQ
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2
32 log 3f x x
Find the Domain, Vertical Asymptote, and x-intercept. Sketch a graph:
Change of base Formula
1) log4 25
2) log2 12
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3
loglog
loga
xx
a
= 2.3219
= 3.5850
To change the base, take the log of the tall over the log of the small.
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
Use properties of logarithms to expand each expression:
1)
2)
3)
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5
5log (5 )x
8
1log
4
72log x
Solve for x.a. b.
Simplify.
c.
log log2 2 3x 4
1log
64x
25log 5
Example: Use the product property to verify: log ( ) log logb b buv u v
2 2 2log 32 log 8 log 4
Use the properties of logarithms to rewrite and simplify the logarithmic expression.
Example
2 42log 4 8
Use the properties of logarithms to expand each expression:
a. b.
Example
log435x y ln
3 5
7
x
Use the properties of logarithms to expand:
Example
4
4logb
x y
z
Use the properties of logarithms to condense
(write as a single log):
Examples
1
23 110 10log log ( )x x
Use the properties of logarithms to condense
(write as a single log):
Examples
1
342 2log log ( )x x
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
Use the properties of logarithms to condense
(write as a single log):
Examples
log 2log 3logcb b bc b z c bc
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
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
HWQ 9/19
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 17
1log log 5
3x x
Condense the expression to the logarithm of a single quantity:
