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(729).

    LHS=RHS
    3 · 729 · Evaluating logarithms

  2. 2. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  3. 3. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms

  4. 4. Evaluate log_3(243).

    LHS=RHS
    3 · 243 · Evaluating logarithms

  5. 5. Evaluate log_6(1296).

    LHS=RHS
    6 · 1296 · Evaluating logarithms

  6. 6. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  7. 7. Evaluate log_2(2).

    LHS=RHS
    2 · 2 · Evaluating logarithms

  8. 8. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  9. 9. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  10. 10. Evaluate log_4(64).

    LHS=RHS
    4 · 64 · Evaluating logarithms

  11. 11. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  12. 12. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms
12 questions · Seed 43 · 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(729).

    6

    Since 3^6 = 729, log_3(729) = 6.

  2. 2. Evaluate log_5(625).

    4

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

  3. 3. Evaluate log_8(4096).

    4

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

  4. 4. Evaluate log_3(243).

    5

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

  5. 5. Evaluate log_6(1296).

    4

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

  6. 6. Evaluate log_4(256).

    4

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

  7. 7. Evaluate log_2(2).

    1

    Since 2^1 = 2, log_2(2) = 1.

  8. 8. Evaluate log_6(6).

    1

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

  9. 9. Evaluate log_6(216).

    3

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

  10. 10. Evaluate log_4(64).

    3

    Since 4^3 = 64, log_4(64) = 3.

  11. 11. Evaluate log_5(5).

    1

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

  12. 12. Evaluate log_7(49).

    2

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

12 questions · Seed 43 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_3(729).

    LHS=RHS
    3 · 729 · Evaluating logarithms

  2. 2. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  3. 3. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms

  4. 4. Evaluate log_3(243).

    LHS=RHS
    3 · 243 · Evaluating logarithms

  5. 5. Evaluate log_6(1296).

    LHS=RHS
    6 · 1296 · Evaluating logarithms

  6. 6. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  7. 7. Evaluate log_2(2).

    LHS=RHS
    2 · 2 · Evaluating logarithms

  8. 8. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  9. 9. Evaluate log_6(216).

    LHS=RHS
    6 · 216 · Evaluating logarithms

  10. 10. Evaluate log_4(64).

    LHS=RHS
    4 · 64 · Evaluating logarithms

  11. 11. Evaluate log_5(5).

    LHS=RHS
    5 · 5 · Evaluating logarithms

  12. 12. Evaluate log_7(49).

    LHS=RHS
    7 · 49 · Evaluating logarithms
12 questions · Seed 43 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_3(729).

    6

    Since 3^6 = 729, log_3(729) = 6.

  2. 2. Evaluate log_5(625).

    4

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

  3. 3. Evaluate log_8(4096).

    4

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

  4. 4. Evaluate log_3(243).

    5

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

  5. 5. Evaluate log_6(1296).

    4

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

  6. 6. Evaluate log_4(256).

    4

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

  7. 7. Evaluate log_2(2).

    1

    Since 2^1 = 2, log_2(2) = 1.

  8. 8. Evaluate log_6(6).

    1

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

  9. 9. Evaluate log_6(216).

    3

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

  10. 10. Evaluate log_4(64).

    3

    Since 4^3 = 64, log_4(64) = 3.

  11. 11. Evaluate log_5(5).

    1

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

  12. 12. Evaluate log_7(49).

    2

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

12 questions · Seed 43 · Age guidance, not curriculum certification