section 9.4 properties of logarithms
DESCRIPTION
Section 9.4 Properties of Logarithms. Review Basic Properties of Logarithms log b 1 =0 log b b= 1 log b b x =x b log bx =x The Product Rule The Power Rule The Quotient Rule Writing Expressions as a Single Logarithm The Change of Base Formula Application. - PowerPoint PPT PresentationTRANSCRIPT
9.4 1
Section 9.4 Properties of Logarithms Review Basic Properties of Logarithms
logb1=0 logbb=1 logbbx=x blogbx=x The Product Rule The Power Rule The Quotient Rule Writing Expressions as a Single Logarithm The Change of Base Formula Application
9.4 2
Basic Properties of Logarithms For any base a (0<a and a≠1) loga1=0
a0 = 1 logaa=1
a1 = a logaax=x
ax = ax
alogax=x ax = logax
9.4 3
The Product Rule for Logs
zyzyyz
xxx
555555
22222
222
loglog3loglog125log125log
log2log100log100log
7log17log2log)72(log14log
64216log4log64log
9.4 4
The Power Rule for Logs
2ln42ln4ln
logloglog
9log59log
log3logloglog)(loglog
42
731
73
7
5
222223
2
31
x
xxx
MMMMMMMM
xx
aa
9.4 5
The Quotient Rule for Logs
3log64loglog64
log
7ln10ln7
10ln
123100log1000log100
1000log
/
4444
xxx
aaa nmnm
9.4 6
Using the Properties Together
23
21
41
logloglogloglog
loglogloglog7log21
)log3log(log41loglog
logloglog3logloglog
77
34
3
33
bbbbxx
bbxx
b
yxz
yzxzyx
zyxzxy
zxy
zyxyzxyzx
aaaaa
aaaaa
aaaaa
bbbbbb
9.4 7
What Next? Conic Sections Present Chapter 10