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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(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  2. 2. Evaluate log_5(125).

    LHS=RHS
    5 · 125 · Evaluating logarithms

  3. 3. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  4. 4. Evaluate log_8(8).

    LHS=RHS
    8 · 8 · Evaluating logarithms

  5. 5. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  6. 6. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  7. 7. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms

  8. 8. Evaluate log_2(4).

    LHS=RHS
    2 · 4 · Evaluating logarithms

  9. 9. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  10. 10. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  11. 11. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  12. 12. Evaluate log_3(3).

    LHS=RHS
    3 · 3 · Evaluating logarithms
12 questions · Seed 104741 · 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(6).

    1

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

  2. 2. Evaluate log_5(125).

    3

    Since 5^3 = 125, log_5(125) = 3.

  3. 3. Evaluate log_7(2401).

    4

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

  4. 4. Evaluate log_8(8).

    1

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

  5. 5. Evaluate log_4(256).

    4

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

  6. 6. Evaluate log_9(9).

    1

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

  7. 7. Evaluate log_7(49).

    2

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

  8. 8. Evaluate log_2(4).

    2

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

  9. 9. Evaluate log_10(1000).

    3

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

  10. 10. Evaluate log_5(5).

    1

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

  11. 11. Evaluate log_3(27).

    3

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

  12. 12. Evaluate log_3(3).

    1

    Since 3^1 = 3, log_3(3) = 1.

12 questions · Seed 104741 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  2. 2. Evaluate log_5(125).

    LHS=RHS
    5 · 125 · Evaluating logarithms

  3. 3. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  4. 4. Evaluate log_8(8).

    LHS=RHS
    8 · 8 · Evaluating logarithms

  5. 5. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  6. 6. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  7. 7. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms

  8. 8. Evaluate log_2(4).

    LHS=RHS
    2 · 4 · Evaluating logarithms

  9. 9. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  10. 10. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  11. 11. Evaluate log_3(27).

    LHS=RHS
    3 · 27 · Evaluating logarithms

  12. 12. Evaluate log_3(3).

    LHS=RHS
    3 · 3 · Evaluating logarithms
12 questions · Seed 104741 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_6(6).

    1

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

  2. 2. Evaluate log_5(125).

    3

    Since 5^3 = 125, log_5(125) = 3.

  3. 3. Evaluate log_7(2401).

    4

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

  4. 4. Evaluate log_8(8).

    1

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

  5. 5. Evaluate log_4(256).

    4

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

  6. 6. Evaluate log_9(9).

    1

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

  7. 7. Evaluate log_7(49).

    2

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

  8. 8. Evaluate log_2(4).

    2

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

  9. 9. Evaluate log_10(1000).

    3

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

  10. 10. Evaluate log_5(5).

    1

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

  11. 11. Evaluate log_3(27).

    3

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

  12. 12. Evaluate log_3(3).

    1

    Since 3^1 = 3, log_3(3) = 1.

12 questions · Seed 104741 · Age guidance, not curriculum certification