Express As a Single Logarithm. Simplify, If Possible

Name______Date______Class______

Practice B

Properties of Logarithms

Express as a single logarithm. Simplify, if possible.

1.log3 9  log3 272.log2 8  log2 163.log10 80  log10 125

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4.log6 8  log6 275.log3 6  log3 13.56.log4 32  log4 128

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Express as a single logarithm. Simplify, if possible.

7.log2 80  log2 108.log10 4000  log10 409.log4 384  log4 6

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10.log2 1920  log2 3011.log3 486  log3 212.log6 180  log6 5

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Simplify, if possible.

13.log4 4614.log5 5 x 515.

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16.17.log8 8518.log3 94

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Evaluate. Round to the nearest hundredth.

19.log12 120.log3 3021.log5 10

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Solve.

22.The Richter magnitude of an earthquake, M, is related to the
energy released in ergs, E, by the formula
Find the energy released by an earthquake of magnitude 4.2.

© Houghton Mifflin Harcourt Publishing Company

Holt McDougal Advanced Algebra

Name______Date______Class______

Properties of Logarithms

Practice A

1.42.64; 64; 6

3.3125; 3125; 54.log10 10,000  4

5.log6 6  16.log8 64  2

7.log5 25  28.log3 3  1

9.log2 32  510.log4 16  2

11.log6 36  212.log5 125  3

13.414.4

15.916.4

17.1218.2

19.1.5920.1.77

21.1.4622.1022 ergs

Practice B

1.log3 243  52.log2 128  7

3.log10 10,000  44.log6 216  3

5.log3 81  46.log4 4096  6

7.log2 8  38.log10 100  2

9.log4 64  310.log2 64  6

11.log3 243  512.log6 36  2

13.614.x 5

15.3016.1

17.518.8

19.020.3.10

21.1.4322.1.26  1018.1 ergs

Practice C

1.log6 216  32.log3 3  1

3.log4 16  24.log6 1296  4

5.log5 125  36.log8 32,768  5

7.log5 625  48.log2 4  2

9.log3 81  410.log8 4096  4

11.log7 7  112.log10 10,000  4

13.614.8x

15.2016.2x 1

17.2x 218.17

19.2.9320.6

21.1222.4.32

23.624.3.32

25.a. log1.06 1.6

b. 8 years

Review for Mastery

1.32.log2 16; 4

3.log9 (3  27); log9 81; 2

4.2  3  65.4  4  16

6.3 log9 81; 3  2  67.5y

8.759.3x

Challenge

1.Both expressions equal .

2.Result is ; formula is easier to compute.

3.Result is ; formula is easier to compute.

4.logab logbc logac

5.

6.log2 32  5; possible answer: using the Chain Rule is much easier.

Problem Solving

1.a.

b. 23.5  log E

c. Yes; by the definition of logarithm; E 1023.5

d. They are both correct; 1023.5 3.16  1023.

2.A3.G

4.C5.F

Reading Strategies

1.True; Product Property

2.True; Quotient Property

3.False; Power Property

4.False: Inverse Property

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Holt McDougal Advanced Algebra