Section 5.5

Properties of Logarithms

OBJECTIVE 1

23

20log 5log 18 3

1

2

1(a) 3 (b) 2 (c) log (d) ln

2e

OBJECTIVE 2

2 32Write log 1 , >1, as a sum of logarithms.

Express all powers as factors.

x x x

4

6 22Write log , 0, as a difference of logarithms.

3

Express all powers as factors.

xx

x

3

2

2Write ln , 2, as a sum and difference of logarithms.

1Express all powers as factors.

x xx

x

OBJECTIVE 3

2

2

Write each of the following as a single logarithm.

3ln 2 ln 2

1log 4 2log 5

2

2log 3 3log 2 log 1

a a

a a a

a x

b

c x

OBJECTIVE 4

3Approximate log 12. Round answer to four decimal places.

7 1

3

Approximate: (a) log 35 (b) log 2

OBJECTIVE 5

5Use a graphing utility to graph log .y x