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

Summary: Today I learned This connects to what I know about What I learned today can help me later when

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