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Total time, \( t = 18 \) hours - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Using the property: \(\log_b(m) + \log_b(n) = \log_b(mn)\):

📌 \log_2(x(x-4)) = 3 \Rightarrow x(x-4) = 2^3 = 8

📌 x^2 - 4x - 8 = 0

📌 Using the quadratic formula:

📌 x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times (-8)}}{2 \times 1}

📌 x = \frac{4 \pm \sqrt{16 + 32}}{2} = \frac{4 \pm \sqrt{48}}{2} = \frac{4 \pm 4\sqrt{3}}{2}

📌 x = 2 \pm 2\sqrt{3}

📌 Since \(x > 4\), \(x = 2 + 2\sqrt{3} \approx 5.464\).

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