вправа 7.3 гдз 11 клас математика Мерзляк Номіровський 2019
Вправа 7.3
Умова:
Умова:
Розв'яжіть нерівність:
Відповідь ГДЗ:
\begin{equation} 1)log_{7}x > 2; \end{equation} \begin{equation} log_{7}x > log_{7}49; \end{equation} \begin{equation} x > 49; \end{equation} \begin{equation} 2)log_{5}x \leq - 1; \end{equation} \begin{equation} log_{5} x\leq log_{5}\frac{1}{5}; \end{equation} \begin{equation} \left\{\begin{matrix} x \leq \frac{1}{5}, \\ x > 0; \end{matrix}\right. \end{equation} \begin{equation} 0 < x \leq \frac{1}{5}; \end{equation} \begin{equation} 3)log_{\frac{1}{2}}x \leq 5; \end{equation} \begin{equation} log_{\frac{1}{2}}x \leq log_{\frac{1}{2}}\frac{1}{32}; \end{equation} \begin{equation} x \geq \frac{1}{32}; \end{equation} \begin{equation} 4)log_{\frac{1}{3}}x > 1; \end{equation} \begin{equation} log_{\frac{1}{3}}x > log_{\frac{1}{3}}\frac{1}{3}; \end{equation} \begin{equation} \left\{\begin{matrix} x < \frac{1}{3}, \\ x > 0; \end{matrix}\right. \end{equation} \begin{equation} 0 < x < \frac{1}{3}; \end{equation} \begin{equation} 5)log_{2}(5x+1) > 4; \end{equation} \begin{equation} log_{2}(5x+1) > log_{2}16; \end{equation} \begin{equation} \left\{\begin{matrix} 5x+1 > 16, \\ 5x+1 > 0; \end{matrix}\right. \end{equation} \begin{equation} 5x > 15; x > 3; \end{equation} \begin{equation} 6)log_{0,6}(x-2) < 2; \end{equation} \begin{equation} log_{0,6}(x-2) < log_{0,6}0,38; \end{equation} \begin{equation} \left\{\begin{matrix} x-2 > 0,36, \\ x-2 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x > 2,36, \\ x > 2; \end{matrix}\right. \end{equation} \begin{equation} x > 2,36; \end{equation} \begin{equation} 7)log_{3}(2x-1) \leq 3; \end{equation} \begin{equation} log_{3}(2x-1) \leq log_{3}27; \end{equation} \begin{equation} \left\{\begin{matrix} 2x-1 \leq 27, \\ 2x-1 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} 2x \leq 28, \\ 2x > 1; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq 14, \\ x > \frac{1}{2}; \end{matrix}\right. \end{equation} \begin{equation} \frac{1}{2} < x \leq 14; \end{equation} \begin{equation} 8)log_{7}(9x+4) \leq 2; \end{equation} \begin{equation} log_{7}(9x+4) \leq log_{7}49; \end{equation} \begin{equation} \left\{\begin{matrix} 9x+4 \leq 49, \\ 9x+4 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} 9x \leq 45 \\ 9x > -4; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq 5 \\ x > -\frac{4}{9}; \end{matrix}\right. \end{equation} \begin{equation} -\frac{4}{9} < x \leq 5; \end{equation} \begin{equation} 9)log_{0,5}(2x+1) \geq -2; \end{equation} \begin{equation} log_{0,5}(2x+1) \geq log_{0,5}4; \end{equation} \begin{equation} \left\{\begin{matrix} 2x+1 \leq 4, \\ 2x+1 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} 2x \leq 3 \\ 2x > -1; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq 1,5, \\ x > -0,5; \end{matrix}\right. \end{equation} \begin{equation} -0,5 < x \leq -1,5; \end{equation} \begin{equation} 10)log_{0,2}(x+6) \geq -1; \end{equation} \begin{equation} log_{0,2}(x+6) \geq log_{0,2}5; \end{equation} \begin{equation} \left\{\begin{matrix} x+6 \leq 5, \\ x+6 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq -1, \\ x > -6; \end{matrix}\right. \end{equation} \begin{equation} -6 < x \leq -1. \end{equation}
\begin{equation} 1)log_{7}x > 2; \end{equation} \begin{equation} log_{7}x > log_{7}49; \end{equation} \begin{equation} x > 49; \end{equation} \begin{equation} 2)log_{5}x \leq - 1; \end{equation} \begin{equation} log_{5} x\leq log_{5}\frac{1}{5}; \end{equation} \begin{equation} \left\{\begin{matrix} x \leq \frac{1}{5}, \\ x > 0; \end{matrix}\right. \end{equation} \begin{equation} 0 < x \leq \frac{1}{5}; \end{equation} \begin{equation} 3)log_{\frac{1}{2}}x \leq 5; \end{equation} \begin{equation} log_{\frac{1}{2}}x \leq log_{\frac{1}{2}}\frac{1}{32}; \end{equation} \begin{equation} x \geq \frac{1}{32}; \end{equation} \begin{equation} 4)log_{\frac{1}{3}}x > 1; \end{equation} \begin{equation} log_{\frac{1}{3}}x > log_{\frac{1}{3}}\frac{1}{3}; \end{equation} \begin{equation} \left\{\begin{matrix} x < \frac{1}{3}, \\ x > 0; \end{matrix}\right. \end{equation} \begin{equation} 0 < x < \frac{1}{3}; \end{equation} \begin{equation} 5)log_{2}(5x+1) > 4; \end{equation} \begin{equation} log_{2}(5x+1) > log_{2}16; \end{equation} \begin{equation} \left\{\begin{matrix} 5x+1 > 16, \\ 5x+1 > 0; \end{matrix}\right. \end{equation} \begin{equation} 5x > 15; x > 3; \end{equation} \begin{equation} 6)log_{0,6}(x-2) < 2; \end{equation} \begin{equation} log_{0,6}(x-2) < log_{0,6}0,38; \end{equation} \begin{equation} \left\{\begin{matrix} x-2 > 0,36, \\ x-2 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x > 2,36, \\ x > 2; \end{matrix}\right. \end{equation} \begin{equation} x > 2,36; \end{equation} \begin{equation} 7)log_{3}(2x-1) \leq 3; \end{equation} \begin{equation} log_{3}(2x-1) \leq log_{3}27; \end{equation} \begin{equation} \left\{\begin{matrix} 2x-1 \leq 27, \\ 2x-1 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} 2x \leq 28, \\ 2x > 1; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq 14, \\ x > \frac{1}{2}; \end{matrix}\right. \end{equation} \begin{equation} \frac{1}{2} < x \leq 14; \end{equation} \begin{equation} 8)log_{7}(9x+4) \leq 2; \end{equation} \begin{equation} log_{7}(9x+4) \leq log_{7}49; \end{equation} \begin{equation} \left\{\begin{matrix} 9x+4 \leq 49, \\ 9x+4 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} 9x \leq 45 \\ 9x > -4; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq 5 \\ x > -\frac{4}{9}; \end{matrix}\right. \end{equation} \begin{equation} -\frac{4}{9} < x \leq 5; \end{equation} \begin{equation} 9)log_{0,5}(2x+1) \geq -2; \end{equation} \begin{equation} log_{0,5}(2x+1) \geq log_{0,5}4; \end{equation} \begin{equation} \left\{\begin{matrix} 2x+1 \leq 4, \\ 2x+1 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} 2x \leq 3 \\ 2x > -1; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq 1,5, \\ x > -0,5; \end{matrix}\right. \end{equation} \begin{equation} -0,5 < x \leq -1,5; \end{equation} \begin{equation} 10)log_{0,2}(x+6) \geq -1; \end{equation} \begin{equation} log_{0,2}(x+6) \geq log_{0,2}5; \end{equation} \begin{equation} \left\{\begin{matrix} x+6 \leq 5, \\ x+6 > 0; \end{matrix}\right. \end{equation} \begin{equation} \left\{\begin{matrix} x \leq -1, \\ x > -6; \end{matrix}\right. \end{equation} \begin{equation} -6 < x \leq -1. \end{equation}