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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_10(10).

    LHS=RHS
    10 · 10 · Evaluating logarithms

  2. 2. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms

  3. 3. Evaluate log_8(512).

    LHS=RHS
    8 · 512 · Evaluating logarithms

  4. 4. Evaluate log_9(729).

    LHS=RHS
    9 · 729 · Evaluating logarithms

  5. 5. Evaluate log_2(16).

    LHS=RHS
    2 · 16 · Evaluating logarithms

  6. 6. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  7. 7. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms

  8. 8. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  9. 9. Evaluate log_8(8).

    LHS=RHS
    8 · 8 · Evaluating logarithms

  10. 10. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  11. 11. Evaluate log_9(81).

    LHS=RHS
    9 · 81 · Evaluating logarithms

  12. 12. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms
12 questions · Seed 104739 · 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_10(10).

    1

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

  2. 2. Evaluate log_7(343).

    3

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

  3. 3. Evaluate log_8(512).

    3

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

  4. 4. Evaluate log_9(729).

    3

    Since 9^3 = 729, log_9(729) = 3.

  5. 5. Evaluate log_2(16).

    4

    Since 2^4 = 16, log_2(16) = 4.

  6. 6. Evaluate log_9(6561).

    4

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

  7. 7. Evaluate log_7(49).

    2

    Since 7^2 = 49, log_7(49) = 2.

  8. 8. Evaluate log_4(256).

    4

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

  9. 9. Evaluate log_8(8).

    1

    Since 8^1 = 8, log_8(8) = 1.

  10. 10. Evaluate log_5(5).

    1

    Since 5^1 = 5, log_5(5) = 1.

  11. 11. Evaluate log_9(81).

    2

    Since 9^2 = 81, log_9(81) = 2.

  12. 12. Evaluate log_3(27).

    3

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

12 questions · Seed 104739 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_10(10).

    LHS=RHS
    10 · 10 · Evaluating logarithms

  2. 2. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms

  3. 3. Evaluate log_8(512).

    LHS=RHS
    8 · 512 · Evaluating logarithms

  4. 4. Evaluate log_9(729).

    LHS=RHS
    9 · 729 · Evaluating logarithms

  5. 5. Evaluate log_2(16).

    LHS=RHS
    2 · 16 · Evaluating logarithms

  6. 6. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  7. 7. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms

  8. 8. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  9. 9. Evaluate log_8(8).

    LHS=RHS
    8 · 8 · Evaluating logarithms

  10. 10. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  11. 11. Evaluate log_9(81).

    LHS=RHS
    9 · 81 · Evaluating logarithms

  12. 12. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms
12 questions · Seed 104739 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_10(10).

    1

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

  2. 2. Evaluate log_7(343).

    3

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

  3. 3. Evaluate log_8(512).

    3

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

  4. 4. Evaluate log_9(729).

    3

    Since 9^3 = 729, log_9(729) = 3.

  5. 5. Evaluate log_2(16).

    4

    Since 2^4 = 16, log_2(16) = 4.

  6. 6. Evaluate log_9(6561).

    4

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

  7. 7. Evaluate log_7(49).

    2

    Since 7^2 = 49, log_7(49) = 2.

  8. 8. Evaluate log_4(256).

    4

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

  9. 9. Evaluate log_8(8).

    1

    Since 8^1 = 8, log_8(8) = 1.

  10. 10. Evaluate log_5(5).

    1

    Since 5^1 = 5, log_5(5) = 1.

  11. 11. Evaluate log_9(81).

    2

    Since 9^2 = 81, log_9(81) = 2.

  12. 12. Evaluate log_3(27).

    3

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

12 questions · Seed 104739 · Age guidance, not curriculum certification