IP3 Class Test (May 2025) Q8 (2023 ACSBR AM Prelim P2 Q8)

IP3 Class Test (May 2025) Q8 (2023 ACSBR AM Prelim P2 Q8)

IP 3
7 marks

It is given that \(\log_{3}(4 - x^{2}) - \log_{\sqrt{3}}(x - 1) = 1\).

  1. Explain clearly why \(1 < x < 2\).[3]
  2. Hence solve \(\log_{3}(4 - x^{2}) - \log_{\sqrt{3}}(x - 1) = 1\) and show that it has only one solution.[4]

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Answer:\(x = \dfrac{3 + \sqrt{13}}{4}\)

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