Indices and Logarithms - II — O/L Mathematics

How do I practise Indices and Logarithms - II?

1 question with a worked solution

1. Solve for x in the logarithmic equation: log₂(x + 5) - log₂(x - 2) = 3.
   1. A) 5
   2. B) 3
   3. C) 2
   4. D) 4
   Check my answer

   Correct answer: B) 3

   Combine logs using quotient rule: log₂((x + 5)/(x - 2)) = 3 → (x + 5)/(x - 2) = 2³ = 8 → x + 5 = 8(x - 2) = 8x - 16 → 7x = 21 → x = 3.

   Show worked solution

   Step 1: Apply quotient law: log_b(M) - log_b(N) = log_b(M/N). Step 2: log₂((x + 5)/(x - 2)) = 3. Step 3: Convert to exponential form: (x + 5)/(x - 2) = 2³ = 8. Step 4: Cross-multiply and solve: x + 5 = 8x - 16 → 7x = 21 → x = 3. Answer: 3.
   Modelled on: the O/L Mathematics examination pattern

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Where does Indices and Logarithms - II fit in the syllabus?

Grade 11 · Term 1