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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_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  2. 2. Evaluate log_3(729).

    LHS=RHS
    3 · 729 · Evaluating logarithms

  3. 3. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms

  4. 4. Evaluate log_7(7).

    LHS=RHS
    7 · 7 · Evaluating logarithms

  5. 5. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  6. 6. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  7. 7. Evaluate log_8(512).

    LHS=RHS
    8 · 512 · Evaluating logarithms

  8. 8. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  9. 9. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  10. 10. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  11. 11. Evaluate log_2(32).

    LHS=RHS
    2 · 32 · Evaluating logarithms

  12. 12. Evaluate log_4(4).

    LHS=RHS
    4 · 4 · Evaluating logarithms
12 questions · Seed 104742 · 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_6(216).

    3

    Since 6^3 = 216, log_6(216) = 3.

  2. 2. Evaluate log_3(729).

    6

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

  3. 3. Evaluate log_4(16).

    2

    Since 4^2 = 16, log_4(16) = 2.

  4. 4. Evaluate log_7(7).

    1

    Since 7^1 = 7, log_7(7) = 1.

  5. 5. Evaluate log_9(9).

    1

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

  6. 6. Evaluate log_5(25).

    2

    Since 5^2 = 25, log_5(25) = 2.

  7. 7. Evaluate log_8(512).

    3

    Since 8^3 = 512, log_8(512) = 3.

  8. 8. Evaluate log_3(81).

    4

    Since 3^4 = 81, log_3(81) = 4.

  9. 9. Evaluate log_4(256).

    4

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

  10. 10. Evaluate log_10(1000).

    3

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

  11. 11. Evaluate log_2(32).

    5

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

  12. 12. Evaluate log_4(4).

    1

    Since 4^1 = 4, log_4(4) = 1.

12 questions · Seed 104742 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  2. 2. Evaluate log_3(729).

    LHS=RHS
    3 · 729 · Evaluating logarithms

  3. 3. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms

  4. 4. Evaluate log_7(7).

    LHS=RHS
    7 · 7 · Evaluating logarithms

  5. 5. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  6. 6. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  7. 7. Evaluate log_8(512).

    LHS=RHS
    8 · 512 · Evaluating logarithms

  8. 8. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  9. 9. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  10. 10. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  11. 11. Evaluate log_2(32).

    LHS=RHS
    2 · 32 · Evaluating logarithms

  12. 12. Evaluate log_4(4).

    LHS=RHS
    4 · 4 · Evaluating logarithms
12 questions · Seed 104742 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_6(216).

    3

    Since 6^3 = 216, log_6(216) = 3.

  2. 2. Evaluate log_3(729).

    6

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

  3. 3. Evaluate log_4(16).

    2

    Since 4^2 = 16, log_4(16) = 2.

  4. 4. Evaluate log_7(7).

    1

    Since 7^1 = 7, log_7(7) = 1.

  5. 5. Evaluate log_9(9).

    1

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

  6. 6. Evaluate log_5(25).

    2

    Since 5^2 = 25, log_5(25) = 2.

  7. 7. Evaluate log_8(512).

    3

    Since 8^3 = 512, log_8(512) = 3.

  8. 8. Evaluate log_3(81).

    4

    Since 3^4 = 81, log_3(81) = 4.

  9. 9. Evaluate log_4(256).

    4

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

  10. 10. Evaluate log_10(1000).

    3

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

  11. 11. Evaluate log_2(32).

    5

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

  12. 12. Evaluate log_4(4).

    1

    Since 4^1 = 4, log_4(4) = 1.

12 questions · Seed 104742 · Age guidance, not curriculum certification