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Home » 3.25x - 60,\!000 = 1,\!200,\!000 - DNSFLEX

3.25x - 60,\!000 = 1,\!200,\!000 - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Résolvez pour \(x\) dans l’équation \(\log_2(x+3) + \log_2(x-1) = 3\).

📌 Utilisez la propriété \(\log_b(m) + \log_b(n) = \log_b(mn)\) :

📌 \log_2((x+3)(x-1)) = 3 \implies (x+3)(x-1) = 2^3 = 8

📌 Développez et résolvez : \(x^2 + 2x - 3 = 8 \implies x^2 + 2x - 11 = 0\).

📌 Utilisez la formule quadratique : \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2} = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3}\).

📌 Puisque \(x > 1\) (pour que les logarithmes soient définis), \(x = -1 + 2\sqrt{3}\).

📌 #### \(-1 + 2\sqrt{3}\)

📌 Une suite géométrique a un premier terme de 3 et une raison commune de 2. Quelle est la somme des 5 premiers termes ?

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