Logarithms

What a logarithm is, and the three laws that turn sums into products, differences into quotients and multiples into powers.

5 sheets · 50 questions · one answer key · 6 pages

Recommended for grades 10–11

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The logarithm Sheet 1 of 5

LogarithmsFinding the logarithm

Name: Date:

Work out each logarithm.

1log₁₀ 1100 =

2log₂ 14 =

3log₃ 243 =

4log₂ 132 =

5log₂ 8192 =

6log₆ 46656 =

7log₄ 1256 =

8log₅ 15625 =

9log₂ 256 =

10log₇ 12401 =

LogarithmsFinding the number

Name: Date:

Find the missing number in each logarithm.

1log₂ = 2

2log₇ = 3

3log₁₀ = 4

4log₂ = 14

5log₃ = 6

6log₂ = 7

7log₉ = 2

8log₃ = 2

9log₇ = 4

10log₉ = 5

Log lawsThe product law

Name: Date:

Write each sum as one logarithm.

1log₅ 2 + log₅ 11 = log₅

2log₃ 7 + log₃ 11 = log₃

3log₁₀ 6 + log₁₀ 10 = log₁₀

4log₃ 3 + log₃ 5 = log₃

5log₅ 2 + log₅ 6 = log₅

6log₂ 6 + log₂ 11 = log₂

7log₂ 4 + log₂ 6 = log₂

8log₁₀ 4 + log₁₀ 5 = log₁₀

9log₁₀ 11 + log₁₀ 11 = log₁₀

10log₂ 5 + log₂ 7 = log₂

Log lawsThe quotient law

Name: Date:

Write each difference as one logarithm.

1log₃ 21 − log₃ 3 = log₃

2log₅ 90 − log₅ 9 = log₅

3log₃ 36 − log₃ 12 = log₃

4log₁₀ 22 − log₁₀ 11 = log₁₀

5log₁₀ 64 − log₁₀ 8 = log₁₀

6log₂ 33 − log₂ 3 = log₂

7log₁₀ 40 − log₁₀ 10 = log₁₀

8log₁₀ 108 − log₁₀ 9 = log₁₀

9log₅ 32 − log₅ 4 = log₅

10log₁₀ 48 − log₁₀ 4 = log₁₀

Log lawsThe power law

Name: Date:

Write each of these as one logarithm.

14 log₅ 3 = log₅

22 log₃ 7 = log₃

32 log₅ 8 = log₅

42 log₃ 12 = log₃

52 log₃ 6 = log₃

62 log₂ 6 = log₂

73 log₁₀ 3 = log₁₀

82 log₃ 2 = log₃

92 log₁₀ 2 = log₁₀

103 log₃ 2 = log₃

Power Pack · LogarithmsAnswer key

The logarithm

1. log₁₀ 1/100 = −22. log₂ 1/4 = −23. log₃ 243 = 54. log₂ 1/32 = −55. log₂ 8192 = 136. log₆ 46656 = 67. log₄ 1/256 = −48. log₅ 15625 = 69. log₂ 256 = 810. log₇ 1/2401 = −4

The number

1. log₂ 4 = 22. log₇ 343 = 33. log₁₀ 10000 = 44. log₂ 16384 = 145. log₃ 729 = 66. log₂ 128 = 77. log₉ 81 = 28. log₃ 9 = 29. log₇ 2401 = 410. log₉ 59049 = 5

A sum → a product

1. log₅ 2 + log₅ 11 = log₅ 222. log₃ 7 + log₃ 11 = log₃ 773. log₁₀ 6 + log₁₀ 10 = log₁₀ 604. log₃ 3 + log₃ 5 = log₃ 155. log₅ 2 + log₅ 6 = log₅ 126. log₂ 6 + log₂ 11 = log₂ 667. log₂ 4 + log₂ 6 = log₂ 248. log₁₀ 4 + log₁₀ 5 = log₁₀ 209. log₁₀ 11 + log₁₀ 11 = log₁₀ 12110. log₂ 5 + log₂ 7 = log₂ 35

A difference → a quotient

1. log₃ 21 − log₃ 3 = log₃ 72. log₅ 90 − log₅ 9 = log₅ 103. log₃ 36 − log₃ 12 = log₃ 3, and that is 14. log₁₀ 22 − log₁₀ 11 = log₁₀ 25. log₁₀ 64 − log₁₀ 8 = log₁₀ 86. log₂ 33 − log₂ 3 = log₂ 117. log₁₀ 40 − log₁₀ 10 = log₁₀ 48. log₁₀ 108 − log₁₀ 9 = log₁₀ 129. log₅ 32 − log₅ 4 = log₅ 810. log₁₀ 48 − log₁₀ 4 = log₁₀ 12

A multiple → a power

1. 4 log₅ 3 = log₅ 812. 2 log₃ 7 = log₃ 493. 2 log₅ 8 = log₅ 644. 2 log₃ 12 = log₃ 1445. 2 log₃ 6 = log₃ 366. 2 log₂ 6 = log₂ 367. 3 log₁₀ 3 = log₁₀ 278. 2 log₃ 2 = log₃ 49. 2 log₁₀ 2 = log₁₀ 410. 3 log₃ 2 = log₃ 8

Logarithms

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