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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(64).

    LHS=RHS
    2 · 64 · Evaluating logarithms

  2. 2. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  3. 3. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  4. 4. Evaluate log_2(16).

    LHS=RHS
    2 · 16 · Evaluating logarithms

  5. 5. Evaluate log_6(36).

    LHS=RHS
    6 · 36 · Evaluating logarithms

  6. 6. Evaluate log_3(9).

    LHS=RHS
    3 · 9 · Evaluating logarithms

  7. 7. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  8. 8. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  9. 9. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  10. 10. Evaluate log_3(243).

    LHS=RHS
    3 · 243 · Evaluating logarithms

  11. 11. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  12. 12. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms
12 questions · Seed 104738 · 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(64).

    6

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

  2. 2. Evaluate log_5(25).

    2

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

  3. 3. Evaluate log_6(216).

    3

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

  4. 4. Evaluate log_2(16).

    4

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

  5. 5. Evaluate log_6(36).

    2

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

  6. 6. Evaluate log_3(9).

    2

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

  7. 7. Evaluate log_9(9).

    1

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

  8. 8. Evaluate log_3(81).

    4

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

  9. 9. Evaluate log_5(5).

    1

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

  10. 10. Evaluate log_3(243).

    5

    Since 3^5 = 243, log_3(243) = 5.

  11. 11. Evaluate log_5(625).

    4

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

  12. 12. Evaluate log_4(16).

    2

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

12 questions · Seed 104738 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_2(64).

    LHS=RHS
    2 · 64 · Evaluating logarithms

  2. 2. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  3. 3. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  4. 4. Evaluate log_2(16).

    LHS=RHS
    2 · 16 · Evaluating logarithms

  5. 5. Evaluate log_6(36).

    LHS=RHS
    6 · 36 · Evaluating logarithms

  6. 6. Evaluate log_3(9).

    LHS=RHS
    3 · 9 · Evaluating logarithms

  7. 7. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  8. 8. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  9. 9. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  10. 10. Evaluate log_3(243).

    LHS=RHS
    3 · 243 · Evaluating logarithms

  11. 11. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  12. 12. Evaluate log_4(16).

    LHS=RHS
    4 · 16 · Evaluating logarithms
12 questions · Seed 104738 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_2(64).

    6

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

  2. 2. Evaluate log_5(25).

    2

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

  3. 3. Evaluate log_6(216).

    3

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

  4. 4. Evaluate log_2(16).

    4

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

  5. 5. Evaluate log_6(36).

    2

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

  6. 6. Evaluate log_3(9).

    2

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

  7. 7. Evaluate log_9(9).

    1

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

  8. 8. Evaluate log_3(81).

    4

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

  9. 9. Evaluate log_5(5).

    1

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

  10. 10. Evaluate log_3(243).

    5

    Since 3^5 = 243, log_3(243) = 5.

  11. 11. Evaluate log_5(625).

    4

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

  12. 12. Evaluate log_4(16).

    2

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

12 questions · Seed 104738 · Age guidance, not curriculum certification