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Home » Solve for \(x\): \(\log_2(x^2 - 5x) = 3\). - Red Crowns

Solve for \(x\): \(\log_2(x^2 - 5x) = 3\). - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 The \(n\)-th term of a geometric sequence is given by \(a_n = a \cdot r^{n-1}\).

📌 Substitute \(a = 5\), \(r = 3\), and \(n = 4\):

📌 \[ a_4 = 5 \cdot 3^{4-1} = 5 \cdot 3^3 = 5 \cdot 27 = 135 \]

📌 Evaluate the integral \(\int (2x^2 + 3x + 1) \, dx\).

📌 \[ \int 2x^2 \, dx = rac{2}{3}x^3, \quad \int 3x \, dx = rac{3}{2}x^2, \quad \int 1 \, dx = x \]

📌 Combine the results:

📌 \[ \int (2x^2 + 3x + 1) \, dx = rac{2}{3}x^3 + rac{3}{2}x^2 + x + C \]

📌 #### \(rac{2}{3}x^3 + rac{3}{2}x^2 + x + C\)

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