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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