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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_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  2. 2. Evaluate log_9(729).

    LHS=RHS
    9 · 729 · Evaluating logarithms

  3. 3. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  4. 4. Evaluate log_10(10000).

    LHS=RHS
    10 · 10000 · Evaluating logarithms

  5. 5. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms

  6. 6. Evaluate log_8(8).

    LHS=RHS
    8 · 8 · Evaluating logarithms

  7. 7. Evaluate log_2(64).

    LHS=RHS
    2 · 64 · Evaluating logarithms

  8. 8. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  9. 9. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  10. 10. Evaluate log_10(100).

    LHS=RHS
    10 · 100 · Evaluating logarithms

  11. 11. Evaluate log_8(64).

    LHS=RHS
    8 · 64 · Evaluating logarithms

  12. 12. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms
12 questions · Seed 104732 · 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_9(9).

    1

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

  2. 2. Evaluate log_9(729).

    3

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

  3. 3. Evaluate log_9(6561).

    4

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

  4. 4. Evaluate log_10(10000).

    4

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

  5. 5. Evaluate log_4(16).

    2

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

  6. 6. Evaluate log_8(8).

    1

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

  7. 7. Evaluate log_2(64).

    6

    Since 2^6 = 64, log_2(64) = 6.

  8. 8. Evaluate log_6(216).

    3

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

  9. 9. Evaluate log_3(27).

    3

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

  10. 10. Evaluate log_10(100).

    2

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

  11. 11. Evaluate log_8(64).

    2

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

  12. 12. Evaluate log_5(625).

    4

    Since 5^4 = 625, log_5(625) = 4.

12 questions · Seed 104732 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  2. 2. Evaluate log_9(729).

    LHS=RHS
    9 · 729 · Evaluating logarithms

  3. 3. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  4. 4. Evaluate log_10(10000).

    LHS=RHS
    10 · 10000 · Evaluating logarithms

  5. 5. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms

  6. 6. Evaluate log_8(8).

    LHS=RHS
    8 · 8 · Evaluating logarithms

  7. 7. Evaluate log_2(64).

    LHS=RHS
    2 · 64 · Evaluating logarithms

  8. 8. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  9. 9. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  10. 10. Evaluate log_10(100).

    LHS=RHS
    10 · 100 · Evaluating logarithms

  11. 11. Evaluate log_8(64).

    LHS=RHS
    8 · 64 · Evaluating logarithms

  12. 12. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms
12 questions · Seed 104732 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_9(9).

    1

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

  2. 2. Evaluate log_9(729).

    3

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

  3. 3. Evaluate log_9(6561).

    4

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

  4. 4. Evaluate log_10(10000).

    4

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

  5. 5. Evaluate log_4(16).

    2

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

  6. 6. Evaluate log_8(8).

    1

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

  7. 7. Evaluate log_2(64).

    6

    Since 2^6 = 64, log_2(64) = 6.

  8. 8. Evaluate log_6(216).

    3

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

  9. 9. Evaluate log_3(27).

    3

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

  10. 10. Evaluate log_10(100).

    2

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

  11. 11. Evaluate log_8(64).

    2

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

  12. 12. Evaluate log_5(625).

    4

    Since 5^4 = 625, log_5(625) = 4.

12 questions · Seed 104732 · Age guidance, not curriculum certification