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' ' NATdrp5995, 11 2023.
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\(x = \frac{27}{11}\) を \(y = 3x - 5\) に代入します：
\[ y = 3\left(\frac{27}{11}\right) - 5 = \frac{81}{11} - \frac{55}{11} = \frac{26}{11} \]
\[ x = \frac{27}{11}, \quad y = \frac{26}{11} \]
#### \(\left(\frac{27}{11}, \frac{26}{11}\right)\)
\(\log_2(x) + \log_2(x - 2) = 3\) のとき、\(x\) の値を求めなさい。
\[ \log_2(x) + \log_2(x - 2) = \log_2[x(x - 2)] \]
\[ \log_2[x(x - 2)] = 3 \]
\[ x(x - 2) = 2^3 = 8 \]
\[ x = \frac{2 \pm \sqrt{(-2)^2 - 4(1)(-8)}}{2(1)} = \frac{2 \pm \sqrt{4 + 32}}{2} = \frac{2 \pm \sqrt{36}}{2} = \frac{2 \pm 6}{2} \]
\[ x = \frac{8}{2} = 4 \quad \text{or} \quad x = \frac{-4}{2} = -2 \]