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voyager star trek seven of nine - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 As \( x \to \infty \), \( f(x) \to \frac{2}{1} = 2 \)

📌 #### Horizontal asymptote: \( y = 2 \)

📌 Solve for \( x \): \( \log_2(x + 3) + \log_2(x - 1) = 3 \)

📌 Use product rule: \( \log_2[(x+3)(x-1)] = 3 \)

📌 So \( (x+3)(x-1) = 2^3 = 8 \)

📌 Expand: \( x^2 + 2x - 3 = 8 \) → \( x^2 + 2x - 11 = 0 \)

📌 Quadratic formula: \( x = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2} = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3} \)

📌 Only \( x = -1 + 2\sqrt{3} \approx 2.46 > 1 \) is valid (domain: \( x > 1 \))

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