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Grade 12 · Functions and Graphs
Logarithms: Definition, Graphs and Solving for n
MEMORANDUM
Name: 
Class: 
Date: 
Mark
  / 16

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)
    (1)
    24 = 16 → 4✓ (1)
  2. 2
    Evaluate log₃ 27. (evaluate)
    (1)
    33 = 27 → 3✓ (1)
  3. 3
    Evaluate log₁₀ 1 000. (evaluate)
    (1)
    103 = 1000 → 3✓ (1)
  4. 4
    Write 53 = 125 in log form. (convert)
    (1)
    log₅ 125 = 3✓ (1)
  5. 5
    Write log₂ 32 = 5 in exponent form. (convert)
    (1)
    25 = 32✓ (1)
  6. 6
    Solve log₂ x = 5. (definition)
    (2)
    x = 25  (1)
    x = 32  (1)    ✓✓ (2)
  7. 7
    Write down the inverse of f(x) = 3x in the form y = … (inverse)
    (2)
    swap x and y: x = 3y  (1)
    y = log₃ x  (1)    ✓✓ (2)
  8. 8
    State the domain and the range of y = log₂ x. (graph)
    (2)
    domain: x > 0  (1)
    range: y ∈ ℝ  (1)    ✓✓ (2)
  9. 9
    Money invested at 8% p.a. compound interest doubles after n years. Find n (2 dp). (finance)
    (2)
    2 = (1,08)n  (1)
    n = log1,08 2 ≈ 9,01 years  (1)    ✓✓ (2)
  10. 10
    Solve 2x = 20 (2 dp). (solve)
    (3)
    x = log₂ 20  (2)
    x ≈ 4,32  (1)    ✓✓✓ (3)
TOTAL: 16 marks
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