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![displaystyle
(frac{1}{3})^{4-2x}=9\\3^{2x-4}=3^2\2x-4=2\x=3;\\\5^{x+2}+5^x=130\25cdot5^x+5^x=130\26cdot5^x=130\5^x=5\x=1;\\\3^{2x+1}-28cdot3^x+9=0\3cdot3^{2x}-28cdot3^x+9=0;big|;3^x=t\3t^2-28t+9=0\\frac{D}{4}:(frac{28}{2})^2-9*3=169=13^2\\t_1,_2=frac{14pm13}{3}; quad t_1=9, quad t_2=frac{1}{3};\\3^x=9 qquad quad 3^2=frac{1}{3}\3^x=3^2quad ; ; quad 3^x=3^{-1}\x=2; qquad quad x=-1. displaystyle
(frac{1}{3})^{4-2x}=9\\3^{2x-4}=3^2\2x-4=2\x=3;\\\5^{x+2}+5^x=130\25cdot5^x+5^x=130\26cdot5^x=130\5^x=5\x=1;\\\3^{2x+1}-28cdot3^x+9=0\3cdot3^{2x}-28cdot3^x+9=0;big|;3^x=t\3t^2-28t+9=0\\frac{D}{4}:(frac{28}{2})^2-9*3=169=13^2\\t_1,_2=frac{14pm13}{3}; quad t_1=9, quad t_2=frac{1}{3};\\3^x=9 qquad quad 3^2=frac{1}{3}\3^x=3^2quad ; ; quad 3^x=3^{-1}\x=2; qquad quad x=-1.](https://tex.z-dn.net/?f=displaystyle%0A%28frac%7B1%7D%7B3%7D%29%5E%7B4-2x%7D%3D9%5C%5C3%5E%7B2x-4%7D%3D3%5E2%5C2x-4%3D2%5Cx%3D3%3B%5C%5C%5C5%5E%7Bx%2B2%7D%2B5%5Ex%3D130%5C25cdot5%5Ex%2B5%5Ex%3D130%5C26cdot5%5Ex%3D130%5C5%5Ex%3D5%5Cx%3D1%3B%5C%5C%5C3%5E%7B2x%2B1%7D-28cdot3%5Ex%2B9%3D0%5C3cdot3%5E%7B2x%7D-28cdot3%5Ex%2B9%3D0%3Bbig%7C%3B3%5Ex%3Dt%5C3t%5E2-28t%2B9%3D0%5C%5Cfrac%7BD%7D%7B4%7D%3A%28frac%7B28%7D%7B2%7D%29%5E2-9%2A3%3D169%3D13%5E2%5C%5Ct_1%2C_2%3Dfrac%7B14pm13%7D%7B3%7D%3B+quad+t_1%3D9%2C+quad+t_2%3Dfrac%7B1%7D%7B3%7D%3B%5C%5C3%5Ex%3D9+qquad+quad+3%5E2%3Dfrac%7B1%7D%7B3%7D%5C3%5Ex%3D3%5E2quad+%3B+%3B+quad+3%5Ex%3D3%5E%7B-1%7D%5Cx%3D2%3B+qquad+quad+x%3D-1.)
Неравенства:
![displaystyle 0,8^{2x-x^2} geq 1\\(frac{4}{5})^{2x-x^2} geq (frac{4}{5})^0\\2x-x^2 leq 0;big|;*(-1)\x(x-2) geq 0\\x_1=0; qquad x_2=2;\\+++0---2+++\\xin(-ifty;0] cup [2; +infty);\\\2^xcdot3^x textgreater 6^{2x^2}cdot frac{1}{6}\6^x textgreater 6^{-1}cdot 6^{2x^2}\6^x textgreater 6^{2x^2-1}\x textgreater 2x^2-1\2x^2-x-1 textless 0\D:1+8=9=3^2\\x_1,_2=frac{1pm3}{4}; qquad x_1=1, qquad x_2=-frac{1}{2};\\+++(-frac{1}{2})---1+++ \\xin (-frac{1}{2};1); displaystyle 0,8^{2x-x^2} geq 1\\(frac{4}{5})^{2x-x^2} geq (frac{4}{5})^0\\2x-x^2 leq 0;big|;*(-1)\x(x-2) geq 0\\x_1=0; qquad x_2=2;\\+++0---2+++\\xin(-ifty;0] cup [2; +infty);\\\2^xcdot3^x textgreater 6^{2x^2}cdot frac{1}{6}\6^x textgreater 6^{-1}cdot 6^{2x^2}\6^x textgreater 6^{2x^2-1}\x textgreater 2x^2-1\2x^2-x-1 textless 0\D:1+8=9=3^2\\x_1,_2=frac{1pm3}{4}; qquad x_1=1, qquad x_2=-frac{1}{2};\\+++(-frac{1}{2})---1+++ \\xin (-frac{1}{2};1);](https://tex.z-dn.net/?f=displaystyle+0%2C8%5E%7B2x-x%5E2%7D+geq+1%5C%5C%28frac%7B4%7D%7B5%7D%29%5E%7B2x-x%5E2%7D+geq+%28frac%7B4%7D%7B5%7D%29%5E0%5C%5C2x-x%5E2++leq++0%3Bbig%7C%3B%2A%28-1%29%5Cx%28x-2%29++geq++0%5C%5Cx_1%3D0%3B+qquad+x_2%3D2%3B%5C%5C%2B%2B%2B0---2%2B%2B%2B%5C%5Cxin%28-ifty%3B0%5D+cup+%5B2%3B+%2Binfty%29%3B%5C%5C%5C2%5Excdot3%5Ex+textgreater++6%5E%7B2x%5E2%7Dcdot+frac%7B1%7D%7B6%7D%5C6%5Ex+textgreater++6%5E%7B-1%7Dcdot+6%5E%7B2x%5E2%7D%5C6%5Ex+textgreater++6%5E%7B2x%5E2-1%7D%5Cx+textgreater++2x%5E2-1%5C2x%5E2-x-1+textless++0%5CD%3A1%2B8%3D9%3D3%5E2%5C%5Cx_1%2C_2%3Dfrac%7B1pm3%7D%7B4%7D%3B+qquad+x_1%3D1%2C+qquad+x_2%3D-frac%7B1%7D%7B2%7D%3B%5C%5C%2B%2B%2B%28-frac%7B1%7D%7B2%7D%29---1%2B%2B%2B+%5C%5Cxin+%28-frac%7B1%7D%7B2%7D%3B1%29%3B)
![displaystyle
7^{x^2+4x} geq (2^x)^{x+4}\7^{x^2+4x} geq 2^{x^2+4x};big|;:2^{x^2+4x}\\(frac{7}{2})^{x^2+4x}=1\\(frac{7}{2})^{x^2+4x}=(frac{7}{2})^0\\x^2+4x geq 0\x(x+4) geq 0\\x_1=0; qquad x_2=-4;\\+++(-4)---0+++\\xin(-infty;-4)cup [0;+infty). displaystyle
7^{x^2+4x} geq (2^x)^{x+4}\7^{x^2+4x} geq 2^{x^2+4x};big|;:2^{x^2+4x}\\(frac{7}{2})^{x^2+4x}=1\\(frac{7}{2})^{x^2+4x}=(frac{7}{2})^0\\x^2+4x geq 0\x(x+4) geq 0\\x_1=0; qquad x_2=-4;\\+++(-4)---0+++\\xin(-infty;-4)cup [0;+infty).](https://tex.z-dn.net/?f=displaystyle%0A7%5E%7Bx%5E2%2B4x%7D+geq+%282%5Ex%29%5E%7Bx%2B4%7D%5C7%5E%7Bx%5E2%2B4x%7D+geq+2%5E%7Bx%5E2%2B4x%7D%3Bbig%7C%3B%3A2%5E%7Bx%5E2%2B4x%7D%5C%5C%28frac%7B7%7D%7B2%7D%29%5E%7Bx%5E2%2B4x%7D%3D1%5C%5C%28frac%7B7%7D%7B2%7D%29%5E%7Bx%5E2%2B4x%7D%3D%28frac%7B7%7D%7B2%7D%29%5E0%5C%5Cx%5E2%2B4x+geq+0%5Cx%28x%2B4%29+geq+0%5C%5Cx_1%3D0%3B+qquad+x_2%3D-4%3B%5C%5C%2B%2B%2B%28-4%29---0%2B%2B%2B%5C%5Cxin%28-infty%3B-4%29cup+%5B0%3B%2Binfty%29.)
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