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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_8(64).

    LHS=RHS
    8 · 64 · Evaluating logarithms

  2. 2. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  3. 3. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  4. 4. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  5. 5. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  6. 6. Evaluate log_6(36).

    LHS=RHS
    6 · 36 · Evaluating logarithms

  7. 7. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  8. 8. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms

  9. 9. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  10. 10. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  11. 11. Evaluate log_10(100).

    LHS=RHS
    10 · 100 · Evaluating logarithms

  12. 12. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms
12 questions · Seed 104736 · 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_8(64).

    2

    Since 8^2 = 64, log_8(64) = 2.

  2. 2. Evaluate log_3(27).

    3

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

  3. 3. Evaluate log_7(2401).

    4

    Since 7^4 = 2401, log_7(2401) = 4.

  4. 4. Evaluate log_9(6561).

    4

    Since 9^4 = 6561, log_9(6561) = 4.

  5. 5. Evaluate log_5(25).

    2

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

  6. 6. Evaluate log_6(36).

    2

    Since 6^2 = 36, log_6(36) = 2.

  7. 7. Evaluate log_4(256).

    4

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

  8. 8. Evaluate log_4(16).

    2

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

  9. 9. Evaluate log_6(216).

    3

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

  10. 10. Evaluate log_6(6).

    1

    Since 6^1 = 6, log_6(6) = 1.

  11. 11. Evaluate log_10(100).

    2

    Since 10^2 = 100, log_10(100) = 2.

  12. 12. Evaluate log_7(343).

    3

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

12 questions · Seed 104736 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_8(64).

    LHS=RHS
    8 · 64 · Evaluating logarithms

  2. 2. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  3. 3. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  4. 4. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  5. 5. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  6. 6. Evaluate log_6(36).

    LHS=RHS
    6 · 36 · Evaluating logarithms

  7. 7. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  8. 8. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms

  9. 9. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  10. 10. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  11. 11. Evaluate log_10(100).

    LHS=RHS
    10 · 100 · Evaluating logarithms

  12. 12. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms
12 questions · Seed 104736 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_8(64).

    2

    Since 8^2 = 64, log_8(64) = 2.

  2. 2. Evaluate log_3(27).

    3

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

  3. 3. Evaluate log_7(2401).

    4

    Since 7^4 = 2401, log_7(2401) = 4.

  4. 4. Evaluate log_9(6561).

    4

    Since 9^4 = 6561, log_9(6561) = 4.

  5. 5. Evaluate log_5(25).

    2

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

  6. 6. Evaluate log_6(36).

    2

    Since 6^2 = 36, log_6(36) = 2.

  7. 7. Evaluate log_4(256).

    4

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

  8. 8. Evaluate log_4(16).

    2

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

  9. 9. Evaluate log_6(216).

    3

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

  10. 10. Evaluate log_6(6).

    1

    Since 6^1 = 6, log_6(6) = 1.

  11. 11. Evaluate log_10(100).

    2

    Since 10^2 = 100, log_10(100) = 2.

  12. 12. Evaluate log_7(343).

    3

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

12 questions · Seed 104736 · Age guidance, not curriculum certification