Kenneth ChengMathematical modeling
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Evaluate using common logarithms.

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TOPIC 01

2024 JM01

The logarithm is of 1/2; it is not log 12.

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01 / Standard#Your turn

Evaluate using common logarithms.

3log⁡(1/2)+log⁡16log⁡4+log⁡5−1\frac{3\log(1/2)+\log16}{\log4+\log5-1}

Official paper · jm01-2024 · I.6 · PDF 2

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A11
  2. Option B−1-1
  3. Option C22
  4. Option D−2-2
  5. Option E44

Working and explanation

BUILD THE REASONING

Hint 1
Write every numerator term using log 2.
Hint 2
Use 1=log 10 in the denominator.
Worked solution

  1. Simplify the numerator.

    3log⁡(1/2)+log⁡16=(−3+4)log⁡2=log⁡23\log(1/2)+\log16=(-3+4)\log2=\log2

  2. Simplify the denominator and divide.

    log⁡4+log⁡5−1=log⁡(20/10)=log⁡2≠0\log4+\log5-1=\log(20/10)=\log2\ne0

A: 1.

Checks and common pitfalls: The logarithm is of 1/2; it is not log 12.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Simplify the numerator.
    3log⁡(1/2)+log⁡16=(−3+4)log⁡2=log⁡23\log(1/2)+\log16=(-3+4)\log2=\log2
  • Simplify the denominator and divide.
    log⁡4+log⁡5−1=log⁡(20/10)=log⁡2≠0\log4+\log5-1=\log(20/10)=\log2\ne0

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