Страница 114 номер 379, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение

1) \(\lg(x^{2} - 2x) = \lg 30 - 1\)
\(\lg(x^{2} - 2x) = \lg \dfrac{30}{10},\)
\(x^{2} - 2x = 3,\)
\(x^{2} - 2x - 3 = 0,\)
\(x_{1{,}2} = \dfrac{2 \pm \sqrt{4 + 12}}{2},\)
\(x_{1} = 3, x_{2} = -1;\)

2) \(\log_{3}(2x^{2} + x) = \log_{3} 6 - \log_{3} 2\)
\(\log_{3}(2x^{2} + x) = \log_{3} \dfrac{6}{2},\)
\(2x^{2} + x - 3 = 0,\)
\(x_{1{,}2} = \dfrac{-1 \pm \sqrt{1 + 24}}{4},\)
\(x_{1} = 1, x_{2} = -\dfrac{3}{2} = -1\dfrac{1}{2};\)

3) \(\lg^{2} x - 3\lg x = 4\)
\(\lg x = z, z^{2} - 3z - 4 = 0,\)
\(z_{1{,}2} = \dfrac{3 \pm \sqrt{9 + 16}}{2},\)
\(z_{1} = 4, z_{2} = -1;\)
\(\lg x = 4, x_{1} = 10^{4};\)
\(\lg x = -1, x_{2} = 0{,}1;\)

4) \(\log_{2}^{2} x - 5\log_{2} x + 6 = 0\)
\(\log_{2} x = z, z^{2} - 5z + 6 = 0,\)
\(z_{1{,}2} = \dfrac{5 \pm \sqrt{25 - 24}}{2},\)
\(z_{1} = 3, z_{2} = 2;\)
\(\log_{2} x = 3, x_{1} = 2^{3} = 8;\)
\(\log_{2} x = 2, x_{2} = 2^{2} = 4.\)