Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
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.

New variationTry interactive challengeBrowse templates

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  2. 2. Evaluate log_8(512).

    LHS=RHS
    8 · 512 · Evaluating logarithms

  3. 3. Evaluate log_6(1296).

    LHS=RHS
    6 · 1296 · Evaluating logarithms

  4. 4. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms

  5. 5. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  6. 6. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  7. 7. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  8. 8. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  9. 9. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  10. 10. Evaluate log_6(36).

    LHS=RHS
    6 · 36 · Evaluating logarithms

  11. 11. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  12. 12. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms
12 questions · Seed 104731 · 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_3(81).

    4

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

  2. 2. Evaluate log_8(512).

    3

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

  3. 3. Evaluate log_6(1296).

    4

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

  4. 4. Evaluate log_7(343).

    3

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

  5. 5. Evaluate log_5(625).

    4

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

  6. 6. Evaluate log_6(6).

    1

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

  7. 7. Evaluate log_10(1000).

    3

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

  8. 8. Evaluate log_9(9).

    1

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

  9. 9. Evaluate log_9(6561).

    4

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

  10. 10. Evaluate log_6(36).

    2

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

  11. 11. Evaluate log_4(256).

    4

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

  12. 12. Evaluate log_7(49).

    2

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

12 questions · Seed 104731 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  2. 2. Evaluate log_8(512).

    LHS=RHS
    8 · 512 · Evaluating logarithms

  3. 3. Evaluate log_6(1296).

    LHS=RHS
    6 · 1296 · Evaluating logarithms

  4. 4. Evaluate log_7(343).

    LHS=RHS
    7 · 343 · Evaluating logarithms

  5. 5. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  6. 6. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  7. 7. Evaluate log_10(1000).

    LHS=RHS
    10 · 1000 · Evaluating logarithms

  8. 8. Evaluate log_9(9).

    LHS=RHS
    9 · 9 · Evaluating logarithms

  9. 9. Evaluate log_9(6561).

    LHS=RHS
    9 · 6561 · Evaluating logarithms

  10. 10. Evaluate log_6(36).

    LHS=RHS
    6 · 36 · Evaluating logarithms

  11. 11. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  12. 12. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms
12 questions · Seed 104731 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_3(81).

    4

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

  2. 2. Evaluate log_8(512).

    3

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

  3. 3. Evaluate log_6(1296).

    4

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

  4. 4. Evaluate log_7(343).

    3

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

  5. 5. Evaluate log_5(625).

    4

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

  6. 6. Evaluate log_6(6).

    1

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

  7. 7. Evaluate log_10(1000).

    3

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

  8. 8. Evaluate log_9(9).

    1

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

  9. 9. Evaluate log_9(6561).

    4

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

  10. 10. Evaluate log_6(36).

    2

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

  11. 11. Evaluate log_4(256).

    4

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

  12. 12. Evaluate log_7(49).

    2

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

12 questions · Seed 104731 · Age guidance, not curriculum certification