april-may 28-1 logarithms (part 2) · a2 4.28 – 5.1 notes section 6-5: properties of logarithms...
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A2 4.28 – 5.1 Notes
Section 6-5: Properties of Logarithms (Part 2)
April-May
28-1 Target 6B We are learning the properties of logarithms so that we can solve logarithmic equations. The properties from last week will help us to evaluate logs that are not base 10 Product Property log log logb b bm n mn+ Quotient Property
log log logb b bmm nn
Power Property
log lognb bm n m
To evaluate, we will use the values given to us for each set of problems. In addition to the ones that are given to use, we can always use
𝒍𝒐𝒈𝒃𝟏 = 𝟎 This will work no matter what number you are given for the base
Use 𝐥𝐨𝐠𝟐 𝟑 = 𝟏. 𝟓𝟖𝟓 and 𝐥𝐨𝐠𝟐 𝟕 = 𝟐. 𝟖𝟎𝟕 to evaluate each logarithm. 1. log2 21 2. log2 3. log2 49 Use 𝒍𝒐𝒈𝟔𝟓 = 𝟎. 𝟖𝟗𝟖 and 𝒍𝒐𝒈𝟔𝟖 = 𝟏. 𝟏𝟔𝟏 to evaluate each logarithm. 4) 𝑙𝑜𝑔 5) 𝑙𝑜𝑔 40 6) 𝑙𝑜𝑔 1 7) 𝑙𝑜𝑔 125 8) 𝑙𝑜𝑔 64 9) 𝑙𝑜𝑔 1
2
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A2 4.28 – 5.1 Practice (Properties of logarithms Part 2)
Use 4log 12 1.1 , 4log 7 0.8 and 4log 8 0.9 to evaluate each logarithm.
1. 47log8
2. 4log 64
3. 41log
12
4. 4log 56
5. 4log 96
6. 42log3
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Worksheet by Kuta Software LLC
Algebra 2
Week 3 Assignment
Name___________________________________
Teacher________________ Period____
-1-
Use the properties of logarithms and the values below to find the logarithm indicated. Do notuse a calculator to evaluate the logs.
1) log 3 8 ≈ 1.9
log 3 10 ≈ 2.1
log 3 11 ≈ 2.2
Find log 3 110
2) log 8 6 ≈ 0.9
log 8 11 ≈ 1.2
log 8 10 ≈ 1.1
Find log 8 121
3) log 6 4 ≈ 0.8
log 6 7 ≈ 1.1
log 6 10 ≈ 1.3
Find log 6 28
4) log 9 4 ≈ 0.6
log 9 11 ≈ 1.1
log 9 6 ≈ 0.8
Find log 9
11
4
5) log 7 9 ≈ 1.1
log 7 12 ≈ 1.3
log 7 10 ≈ 1.2
Find log 7
1
81
6) log 9 6 ≈ 0.8
log 9 4 ≈ 0.6
log 9 5 ≈ 0.7
Find log 9
1
5
7) log 9 5 ≈ 0.7
log 9 8 ≈ 0.9
log 9 6 ≈ 0.8
Find log 9 48
8) log 4 9 ≈ 1.6
log 4 6 ≈ 1.3
log 4 11 ≈ 1.7
Find log 4 121
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Worksheet by Kuta Software LLC-2-
9) log 3 10 ≈ 2.1
log 3 4 ≈ 1.3
log 3 7 ≈ 1.8
Find log 3
1
16
10) log 12 ≈ 1.1log 8 ≈ 0.9log 7 ≈ 0.8Find log 64
11) log 7 ≈ 0.8log 8 ≈ 0.9log 12 ≈ 1.1
Find log7
12
12) log 8 ≈ 0.9log 7 ≈ 0.8log 12 ≈ 1.1Find log 144
Rewrite each logarithm using the "Power Property of Logarithms"
13) log 11 x5 14) log 3 v
16
15) log 6 13x 16) log 2 a9
17) log x2 18) log 8 6x
19) log 7 3x 20) ln x4
21) log 4 57x
Solution Bank to Week 4 Assignment
-0.3 𝑥 log 13 3.4 2.2 4 ln 𝑥 2 log 𝑥 -2.6 9 log 𝑎 2.4
𝑥 log 6 0.5 5 log11 𝑥
-0.7 4.3 1.9 1.8 1.7 𝑥 log 3
16 log 𝑣 𝑥 log 57 -2.2