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Home » $ k = 3 $: $ 370^\circ $ → too large - Nurtured Nest

$ k = 3 $: $ 370^\circ $ → too large - Nurtured Nest

📅 May 8, 2026 👤 scraface

May 08, 2026

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#### #### 62
If \( \log_2(x) + \log_2(x - 4) = 3 \), find \( x \).
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...
x = 2 \pm 2\sqrt{3}
Since \(x > 4\), \(x = 2 + 2\sqrt{3} \approx 5.464\).

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