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📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Solve for \( x \) in the equation \( \log_2(x+1) + \log_2(x-1) = 3 \).

📌 Combine logs: \( \log_2((x+1)(x-1)) = 3 \).

📌 So, \( (x+1)(x-1) = 2^3 = 8 \).

📌 Then \( x^2 - 1 = 8 \).

📌 \( x^2 = 9 \), so \( x = \pm 3 \).

📌 Since \( x-1 > 0 \), \( x > 1 \), thus \( x = 3 \).

📌 The function \( f(x) = rac{2x^2 - 3x + 1}{x - 1} \) has a removable discontinuity. Find the value of \( f(1) \) after removing the discontinuity.

📌 Factor numerator: \( 2x^2 - 3x + 1 = (2x - 1)(x - 1) \).

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