Notes Over 8.5Properties of Logarithms

Product Property

Quotient Property

Power Property

uvblog ublog vblog

v

ublog ublog vblog

nbulog n ublog

Notes Over 8.5Using Properties of Logarithms

to285.110log and 774.04log Use 66

40log .1 6

104log6 10log4log 66

774.0

.expression theof value theeapproximat

285.1059.2

100log .2 62

610log10log 2 6

285.1257.2

Notes Over 8.5Using Properties of Logarithms

to285.110log and 774.04log Use 66

4

10log .3 6

4log10log 66 774.0

.expression theof value theeapproximat

285.1511.0

64log .4 63

6 4log4log 3 6

774.03322.2

Notes Over 8.5Expanding a Logarithmic Expression

x9 log .5x log9 log

Expand the expression.3

2 6 log .6 x3

22 log6 log x6 log2 x log 3 2

3

2 log .7 6

3 log2 log 66

Notes Over 8.5Expanding a Logarithmic Expression

5

4 log .8 3

x

5 log4 log 33 x

Expand the expression.

x log4 log 33 5 log3xy2ln .9

2ln xln yln

Notes Over 8.5Expanding a Logarithmic Expression

y

x22ln .10

yx ln 2ln 2

Expand the expression.

2ln 2ln x yln

2ln yln xln 2

Notes Over 8.5Condensing a Logarithmic Expression

5 log 21 log .11 44 521 log4

Condense the expression.

60 log4

yx log log .12

y

x log

Notes Over 8.5Condensing a Logarithmic Expression

9ln 6ln 3ln .13 9ln 63ln

Condense the expression.

9

81ln

3 log 3 .14 2

32 3 log

2ln

72 log2

Notes Over 8.5Condensing a Logarithmic Expression

xx log 3 log 6 .15 22 6

2 log x

Condense the expression.

362 log xx

2ln 3 42ln .16 42ln

92 log x

8

42ln

32 log x

32ln 3ln

Notes Over 8.5Using the Change-of-Base Formula

30 log .17 3 3 log

03 log

Use the change-of-base formula to evaluate the expression.

096.3477.1

477.0

13 log .18 44 log

31 log 850.1

114.1

602.0

Notes Over 8.5Using the Change-of-Base Formula

17 log .19 2 2 log

71 log

Use the change-of-base formula to evaluate the expression.

086.4230.1

301.0

10 log .20 55 log

01 log 431.1

1

699.0

Notes Over 8.5