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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(1296).

    LHS=RHS
    6 · 1296 · Evaluating logarithms

  2. 2. Evaluate log_5(125).

    LHS=RHS
    5 · 125 · Evaluating logarithms

  3. 3. Evaluate log_4(4).

    LHS=RHS
    4 · 4 · Evaluating logarithms

  4. 4. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  5. 5. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  6. 6. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  7. 7. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  8. 8. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  9. 9. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms

  10. 10. Evaluate log_7(7).

    LHS=RHS
    7 · 7 · Evaluating logarithms

  11. 11. Evaluate log_3(3).

    LHS=RHS
    3 · 3 · Evaluating logarithms

  12. 12. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms
12 questions · Seed 104733 · 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(1296).

    4

    Since 6^4 = 1296, log_6(1296) = 4.

  2. 2. Evaluate log_5(125).

    3

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

  3. 3. Evaluate log_4(4).

    1

    Since 4^1 = 4, log_4(4) = 1.

  4. 4. Evaluate log_5(25).

    2

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

  5. 5. Evaluate log_5(5).

    1

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

  6. 6. Evaluate log_5(625).

    4

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

  7. 7. Evaluate log_7(2401).

    4

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

  8. 8. Evaluate log_9(9).

    1

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

  9. 9. Evaluate log_8(4096).

    4

    Since 8^4 = 4096, log_8(4096) = 4.

  10. 10. Evaluate log_7(7).

    1

    Since 7^1 = 7, log_7(7) = 1.

  11. 11. Evaluate log_3(3).

    1

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

  12. 12. Evaluate log_9(6561).

    4

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

12 questions · Seed 104733 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_6(1296).

    LHS=RHS
    6 · 1296 · Evaluating logarithms

  2. 2. Evaluate log_5(125).

    LHS=RHS
    5 · 125 · Evaluating logarithms

  3. 3. Evaluate log_4(4).

    LHS=RHS
    4 · 4 · Evaluating logarithms

  4. 4. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  5. 5. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  6. 6. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  7. 7. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  8. 8. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  9. 9. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms

  10. 10. Evaluate log_7(7).

    LHS=RHS
    7 · 7 · Evaluating logarithms

  11. 11. Evaluate log_3(3).

    LHS=RHS
    3 · 3 · Evaluating logarithms

  12. 12. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms
12 questions · Seed 104733 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_6(1296).

    4

    Since 6^4 = 1296, log_6(1296) = 4.

  2. 2. Evaluate log_5(125).

    3

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

  3. 3. Evaluate log_4(4).

    1

    Since 4^1 = 4, log_4(4) = 1.

  4. 4. Evaluate log_5(25).

    2

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

  5. 5. Evaluate log_5(5).

    1

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

  6. 6. Evaluate log_5(625).

    4

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

  7. 7. Evaluate log_7(2401).

    4

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

  8. 8. Evaluate log_9(9).

    1

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

  9. 9. Evaluate log_8(4096).

    4

    Since 8^4 = 4096, log_8(4096) = 4.

  10. 10. Evaluate log_7(7).

    1

    Since 7^1 = 7, log_7(7) = 1.

  11. 11. Evaluate log_3(3).

    1

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

  12. 12. Evaluate log_9(6561).

    4

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

12 questions · Seed 104733 · Age guidance, not curriculum certification