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Home » The area \( A \) of a right triangle with legs \( a \) and \( b \) is: - Nelissen Grade advocaten

The area \( A \) of a right triangle with legs \( a \) and \( b \) is: - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 If \( \log_2(x) + \log_2(x - 3) = 2 \), find the value of \( x \).

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

📌 Rewrite: \( x(x - 3) = 2^2 = 4 \).

📌 Expand: \( x^2 - 3x - 4 = 0 \).

📌 Factor: \( (x - 4)(x + 1) = 0 \), so \( x = 4 \) (since \( x > 3 \) for log to be defined).

📌 Find the derivative of \( y = \ln(x^2 + 1) \) at \( x = 1 \).

📌 Use chain rule: \( rac{dy}{dx} = rac{1}{x^2 + 1} \cdot 2x = rac{2x}{x^2 + 1} \).

📌 Evaluate at \( x = 1 \): \( rac{2(1)}{1^2 + 1} = rac{2}{2} = 1 \).

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