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Possible solutions: \(n = \frac{54}{6} = 9\) and \(n = \frac{-68}{6}\) (not valid as \(n\) must be positive).
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#### \(n = 9\)
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3.
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A circle is inscribed in a square. If the side of the square is 10 units find the area of the circle.
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The diameter of the circle is equal to the side of the square which is 10 units.
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Thus the radius \(r = \frac{10}{2} = 5\) units.
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The area of the circle is \(A = \pi r^2 = \pi \times 5^2 = 25\pi\).
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#### \(25\pi\)
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4.
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Solve for \(x\) in the equation \(\log_2(x+1) + \log_2(x-1) = 3\).
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Combine the logarithms: \(\log_2((x+1)(x-1)) = 3\).
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This implies \((x+1)(x-1) = 2^3 = 8\).
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