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\frac1u^2 + \frac2u + 1 + 2u - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 Question**: If \( \log_2(x) + \log_2(x - 2) = 3 \), find \( x \).

📌 Combine logs: \( \log_2(x(x - 2)) = 3 \).

📌 So, \( x(x - 2) = 2^3 = 8 \).

📌 \( x^2 - 2x - 8 = 0 \).

📌 Factor: \( (x - 4)(x + 2) = 0 \).

📌 \( x = 4 \) or \( x = -2 \).

📌 But \( x > 2 \) for log to be defined, so \( x = 4 \).

📌 The solution is \( x = 4 \).

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