Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 354

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\[1)\ y = \lg(3x - 2)\]

\[3x - 2 > 0\]

\[3x > 2\ \]

\[x > \frac{2}{3}\]

\[Ответ:\ \ x > \frac{2}{3}.\]

\[2)\ y = \log_{2}(7 - 5x)\]

\[7 - 5x > 0\]

\[5x < 7\]

\[x < 1,4\]

\[Ответ:\ \ x < 1,4.\]

\[3)\ y = \log_{\frac{1}{2}}\left( x^{2} - 2 \right)\]

\[x^{2} - 2 > 0\]

\[x^{2} > 2\]

\[x < - \sqrt{2}\ ;\text{\ \ }x > \sqrt{2}.\]

\[Ответ:\ \ x < - \sqrt{2};\ x > \sqrt{2}.\]

\[4)\ y = \log_{7}{(4 - x^{2})}\]

\[4 - x^{2} > 0\]

\[x^{2} - 4 < 0\]

\[(x + 2)(x - 2) < 0\]

\[- 2 < x < 2\]

\[Ответ:\ \ - 2 < x < 2.\]