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Grade 12 · Functions
Logarithms: The Complete Grade 12 Guide
MEMORANDUM
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Class: 
Date: 
Mark
  / 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Evaluate log₂ 16. (evaluate)
    (2)
    24 = 16 → 4✓✓ (2)
  2. 2
    Evaluate log₃ 27. (evaluate)
    (2)
    33 = 27 → 3✓✓ (2)
  3. 3
    Evaluate log₁₀ 1000. (evaluate)
    (2)
    103 = 1000 → 3✓✓ (2)
  4. 4
    Write 53 = 125 in log form. (convert)
    (2)
    log₅ 125 = 3✓✓ (2)
  5. 5
    Write log₂ 32 = 5 in exponent form. (convert)
    (2)
    25 = 32✓✓ (2)
  6. 6
    Simplify log 2 + log 50. (laws)
    (2)
    log(2×50) = log 100 = 2✓✓ (2)
  7. 7
    Simplify log 200 − log 2. (laws)
    (2)
    log(2002) = log 100 = 2✓✓ (2)
  8. 8
    Write log 8 as a multiple of log 2. (laws)
    (2)
    log 23 = 3 log 2✓✓ (2)
  9. 9
    Evaluate log₂ 10 (change of base, 2 dp). (change base)
    (2)
    log10 ÷ log2 ≈ 3,32✓✓ (2)
  10. 10
    Solve 2ˣ = 20 (2 dp). (solve)
    (2)
    x = log20 ÷ log2 ≈ 4,32✓✓ (2)
TOTAL: 20 marks
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