\( x > 3 \) であるため、有効な解は \( x = 4 \) です。
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- 対数を組み合わせます：\( \log_2(x(x-3)) = 3 \)。
- 指数形式に変換します：\( x(x-3) = 2^3 = 8 \)。
- 因数分解：\( (x-4)(x+2) = 0 \)，したがって \( x = 4 \) または \( x = -2 \) です。
- 三角形の面積 \( A \) は \( \frac{1}{2} \times 6 \times 8 = 24 \) cm² です。
- 半周長 \( s \) は \( \frac{6 + 8 + 10}{2} = 12 \) cm です（ピタゴラスの定理で斜辺は10 cm）。
- 内接円の半径 \( r \) は \( r = \frac{A}{s} = \frac{24}{12} = 2 \) cm です。
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