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MathsAges 16-18

Evaluating logarithms

Evaluate base-b logarithms of exact integer powers using log_b(bⁿ) = n. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_2(32).

    LHS=RHS
    2 · 32 · Evaluating logarithms

  2. 2. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  3. 3. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  4. 4. Evaluate log_3(9).

    LHS=RHS
    3 · 9 · Evaluating logarithms

  5. 5. Evaluate log_2(8).

    LHS=RHS
    2 · 8 · Evaluating logarithms

  6. 6. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms

  7. 7. Evaluate log_10(10).

    LHS=RHS
    10 · 10 · Evaluating logarithms

  8. 8. Evaluate log_10(10000).

    LHS=RHS
    10 · 10000 · Evaluating logarithms

  9. 9. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms

  10. 10. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  11. 11. Evaluate log_3(729).

    LHS=RHS
    3 · 729 · Evaluating logarithms

  12. 12. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms
12 questions · Seed 104735 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_2(32).

    5

    Since 2^5 = 32, log_2(32) = 5.

  2. 2. Evaluate log_10(1000).

    3

    Since 10^3 = 1000, log_10(1000) = 3.

  3. 3. Evaluate log_3(27).

    3

    Since 3^3 = 27, log_3(27) = 3.

  4. 4. Evaluate log_3(9).

    2

    Since 3^2 = 9, log_3(9) = 2.

  5. 5. Evaluate log_2(8).

    3

    Since 2^3 = 8, log_2(8) = 3.

  6. 6. Evaluate log_8(4096).

    4

    Since 8^4 = 4096, log_8(4096) = 4.

  7. 7. Evaluate log_10(10).

    1

    Since 10^1 = 10, log_10(10) = 1.

  8. 8. Evaluate log_10(10000).

    4

    Since 10^4 = 10000, log_10(10000) = 4.

  9. 9. Evaluate log_7(343).

    3

    Since 7^3 = 343, log_7(343) = 3.

  10. 10. Evaluate log_9(9).

    1

    Since 9^1 = 9, log_9(9) = 1.

  11. 11. Evaluate log_3(729).

    6

    Since 3^6 = 729, log_3(729) = 6.

  12. 12. Evaluate log_4(256).

    4

    Since 4^4 = 256, log_4(256) = 4.

12 questions · Seed 104735 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_2(32).

    LHS=RHS
    2 · 32 · Evaluating logarithms

  2. 2. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  3. 3. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  4. 4. Evaluate log_3(9).

    LHS=RHS
    3 · 9 · Evaluating logarithms

  5. 5. Evaluate log_2(8).

    LHS=RHS
    2 · 8 · Evaluating logarithms

  6. 6. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms

  7. 7. Evaluate log_10(10).

    LHS=RHS
    10 · 10 · Evaluating logarithms

  8. 8. Evaluate log_10(10000).

    LHS=RHS
    10 · 10000 · Evaluating logarithms

  9. 9. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms

  10. 10. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  11. 11. Evaluate log_3(729).

    LHS=RHS
    3 · 729 · Evaluating logarithms

  12. 12. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms
12 questions · Seed 104735 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_2(32).

    5

    Since 2^5 = 32, log_2(32) = 5.

  2. 2. Evaluate log_10(1000).

    3

    Since 10^3 = 1000, log_10(1000) = 3.

  3. 3. Evaluate log_3(27).

    3

    Since 3^3 = 27, log_3(27) = 3.

  4. 4. Evaluate log_3(9).

    2

    Since 3^2 = 9, log_3(9) = 2.

  5. 5. Evaluate log_2(8).

    3

    Since 2^3 = 8, log_2(8) = 3.

  6. 6. Evaluate log_8(4096).

    4

    Since 8^4 = 4096, log_8(4096) = 4.

  7. 7. Evaluate log_10(10).

    1

    Since 10^1 = 10, log_10(10) = 1.

  8. 8. Evaluate log_10(10000).

    4

    Since 10^4 = 10000, log_10(10000) = 4.

  9. 9. Evaluate log_7(343).

    3

    Since 7^3 = 343, log_7(343) = 3.

  10. 10. Evaluate log_9(9).

    1

    Since 9^1 = 9, log_9(9) = 1.

  11. 11. Evaluate log_3(729).

    6

    Since 3^6 = 729, log_3(729) = 6.

  12. 12. Evaluate log_4(256).

    4

    Since 4^4 = 256, log_4(256) = 4.

12 questions · Seed 104735 · Age guidance, not curriculum certification