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Home » Compound Interest formula: \( A = P \left(1 + \fracr100\right) \) - Silent Sales Machine

Compound Interest formula: \( A = P \left(1 + \fracr100\right) \) - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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: \( x > 1 \))

📌 #### \( x = -1 + 2\sqrt{3} \)

📌 Find the sum of the infinite geometric series with first term 5 and common ratio \( \frac{2}{3} \).

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