Kenneth ChengMathematical modeling
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Express the logarithm using p and q.

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TOPIC 01

2025 JM01

The extra factor 2 in the denominator contributes −1.

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01 / Standard#Your turn

Express the logarithm using p and q.

2p=5,2q=7,log⁡2(0.7)2^p=5,\quad2^q=7,\quad\log_2(0.7)

Official paper · jm01-2025 · I.5 · PDF 2

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

Skills and prerequisite lessons
  1. Option Aq+p−1q+p-1
  2. Option B2q−2p2q-2p
  3. Option Cq−p+1q-p+1
  4. Option Dq−p−1q-p-1
  5. None of these

Working and explanation

BUILD THE REASONING

Hint 1
Write 0.7 as 7/(2·5).
Hint 2
Turn division into subtraction of logarithms.
Worked solution

  1. Identify the known logarithms.

    p=log⁡25,q=log⁡27p=\log_2 5,\quad q=\log_2 7

  2. Split the quotient.

    log⁡272⋅5=q−1−p\log_2\frac7{2\cdot5}=q-1-p

D: q−p−1.

Checks and common pitfalls: The extra factor 2 in the denominator contributes −1.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Identify the known logarithms.
    p=log⁡25,q=log⁡27p=\log_2 5,\quad q=\log_2 7
  • Split the quotient.
    log⁡272⋅5=q−1−p\log_2\frac7{2\cdot5}=q-1-p

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