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Home » a^4 + b^4 = 1^2 - 2 \cdot \frac14 = 1 - \frac12 = \frac12 - Appfinity Technologies

a^4 + b^4 = 1^2 - 2 \cdot \frac14 = 1 - \frac12 = \frac12 - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A line passes through the points \( (3, 7) \) and \( (-1, -5) \). What is the slope of a line perpendicular to this line?

📌 The slope of the original line is \( m = \frac{7 - (-5)}{3 - (-1)} = \frac{12}{4} = 3 \).

📌 The slope of a perpendicular line is the negative reciprocal: \( -\frac{1}{3} \).

📌 Using logarithmic properties: \( \log_2(x(x - 2)) = 3 \).

📌 Then, \( x^2 - 2x - 8 = 0 \).

📌 Factoring: \( (x - 4)(x + 2) = 0 \).

📌 So, \( x = 4 \) or \( x = -2 \).

📌 Since \( x > 2 \) for the logs to be defined, \( x = 4 \).

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