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

Question

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

Accepted Answer

$x = \dfrac{3 + \sqrt{13}}{4}$

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

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

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