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If \(\log_2(x) + \log_2(x-3) = 3\), what is x?
Combine logs: \(\log_2(x(x-3)) = 3\)
Convert to exponential: \(x(x-3) = 2^3 = 8\)
Solve quadratic: \(x^2 - 3x - 8 = 0\)
Factor: \((x-4)(x+2) = 0\)
Solutions: x = 4 or x = -2 (discard negative)
Valid x: 4
Circumference formula: \(C = 2\pi r\)
Solve for r: \(31.4 = 2\pi r \Rightarrow r = \frac{31.4}{2\pi} \approx 5\)
Area formula: \(A = \pi r^2\)