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