7.4Practice
Writeeachequationinlogarithmicform.
5.𝑏 " = 𝑥 + 5
3. 61 = 6 1
8
1. 8−1 = 4. 6−3 =
2. 11 = 1 0
1
216
Writeeachequationinexponentialform.
6. 3 = log 2 8 8.−2=log0.01
7.log0.1=−1
9. log 49 7 = 10. log 2 128 = 7 1
2
11.log * 𝑏𝑚 = 𝑦
Evaluatethelogarithmwithoutacalculator.Showyourwork.
12.log - 2
16.log 4 1
20.log 6 6- 13.log/0 17
17.log * 1
21.log * 𝑏 8 14.log * 𝑏
18.log - 24 15.log 3 1
19.log 5 54 Determineifeachstatementistrueorfalse.Statewhatpropertyorpropertiesarebeingusedand
writethecorrectrelationshipifnecessary.
22.log12=log4+log3
1
25. log 4 4 x = log 4 2 x 3 log 3
2
23. log =
5
log 5
24. log 6 12 + log 6 3 = 2 /
;
26. log 4 162 − log 4 2 = 1
9
Writeeachlogarithmasaquotientoftwocommonlogarithmsusingthechangeofbaseformula
andsimplifyifpossible.Thenuseacalculatortoestimatetothenearesthundredth.
27. log 4 12 29. log 5 16 28. log 2 1000 30. log100 5
Writeeachlogarithmasaquotientoftwologarithmsbase2usingthechangeofbaseformula.
Simplifyyouranswerwithoutacalculator.
31.log 4- 4
33.log 3 16
32.log 9 32
34.log/6 8
Usethechangeofbaseformulatosimplifyeachexpressionwithoutacalculator.
/
35.log -0 9
37.log 9 3
36.log -5 125
/
38.log/6 -
Answers
/
1.log 3 = −1
3
22.True.ProductProperty
4
23.False.QuotientProperty:log = log 3 − log 5or
5
2.log// 1 = 0
ChangeofBase:
3.log 6 6 = 1
24.True.ProductProperty.
4.log 6
/
-/6
= −3
6.24 = 8
7.10
-
26.True.QuotientandPowerProperty.
27.
FGH /FGH 9
28.
FGH -
9.49 = 7
29.
FGH /6
11.𝑏 EA/ = 𝑚
30.
FGH 5
12.1
31. 0
10.2 = 128
FGH 5
5
5
32. 9
33. 15.0
4
4
34. 9
-
16.0
35. 17.0
36. 18.3
19.3
20.2
21.x
4
4
-
4
37.− /
38.− 9
≈ 1.79
4 FGH /J
C
D
14.1
= log 5 3
25.False. log 9 4𝑥 - = log 9 2𝑥
= 0.1
8.10A- = 0.01
13.1
FGH 5
/
5.log * 𝑥 + 5 = 𝑚
A/
FGH 4
≈ 9.97
≈ 1.72
≈ 0.35