[tex]\displaystyle\bf\\3)\\\\19^{x^{2} -4x-21} =1\\\\19^{x^{2} -4x-21} =19^\circ\\\\x^{2} -4x-21=0\\\\D=(-4)^{2} -4\cdot(-21)=16+84=100=10^{2} \\\\\\x_{1} =\frac{4-10}{2} =\frac{-6}{2} =-3\\\\\\x_{2} =\frac{4+10}{2} =\frac{14}{2} =7\\\\\\Otvet \ : \ -3 \ ; \ 7\\\\\\4)\\\\27^{x} =81\\\\\Big(3^{3} \Big)^{x} =3^{4} \\\\3^{3x} =3^{4} \\\\3x=4\\\\x=1\frac{1}{3} \\\\Otvet \ : \ 1\frac{1}{3}[/tex]
[tex]\displaystyle\bf\\1)\\\\7^{x} < \frac{1}{49} \\\\7^{x} < 7^{-2} \\\\7 > 0 \ \ \ \Rightarrow \ \ \ x < -2\\\\Otvet \ : \ x\in\Big(-\infty \ ; \ -2\Big)\\\\\\2)\\\\\Big(0,1\Big)^{x} > 0,001\\\\\Big(0,1\Big)^{x} > \Big(0,1)^{3} \\\\0 < 0,1 < 1 \ \ \ \Rightarrow \ \ \ x < 3\\\\Otvet \ : \ x\in\Big(-\infty \ ; \ 3\Big)[/tex]
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[tex]\displaystyle\bf\\3)\\\\19^{x^{2} -4x-21} =1\\\\19^{x^{2} -4x-21} =19^\circ\\\\x^{2} -4x-21=0\\\\D=(-4)^{2} -4\cdot(-21)=16+84=100=10^{2} \\\\\\x_{1} =\frac{4-10}{2} =\frac{-6}{2} =-3\\\\\\x_{2} =\frac{4+10}{2} =\frac{14}{2} =7\\\\\\Otvet \ : \ -3 \ ; \ 7\\\\\\4)\\\\27^{x} =81\\\\\Big(3^{3} \Big)^{x} =3^{4} \\\\3^{3x} =3^{4} \\\\3x=4\\\\x=1\frac{1}{3} \\\\Otvet \ : \ 1\frac{1}{3}[/tex]
[tex]\displaystyle\bf\\1)\\\\7^{x} < \frac{1}{49} \\\\7^{x} < 7^{-2} \\\\7 > 0 \ \ \ \Rightarrow \ \ \ x < -2\\\\Otvet \ : \ x\in\Big(-\infty \ ; \ -2\Big)\\\\\\2)\\\\\Big(0,1\Big)^{x} > 0,001\\\\\Big(0,1\Big)^{x} > \Big(0,1)^{3} \\\\0 < 0,1 < 1 \ \ \ \Rightarrow \ \ \ x < 3\\\\Otvet \ : \ x\in\Big(-\infty \ ; \ 3\Big)[/tex]