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№1.
![( frac{14}{23})^{x+ frac{2}{ sqrt{x}} }=( frac{23}{14} )^{ frac{5}{ sqrt{x}}-x-1 } \ \ ( frac{14}{23})^{x+ frac{2}{ sqrt{x}} }=( frac{14}{23} )^{ -frac{5}{ sqrt{x}}+x+1 } \ \ x+ frac{2}{ sqrt{x} }= -frac{5}{ sqrt{x}}+x+1 \ \ frac{2}{ sqrt{x} }+ frac{5}{ sqrt{x} }+x-x=1 \ \ frac{2+5}{ sqrt{x} }=1 \ \ frac{7}{ sqrt{x} }=1 \ \ sqrt{x} =7 \ x=49 ( frac{14}{23})^{x+ frac{2}{ sqrt{x}} }=( frac{23}{14} )^{ frac{5}{ sqrt{x}}-x-1 } \ \ ( frac{14}{23})^{x+ frac{2}{ sqrt{x}} }=( frac{14}{23} )^{ -frac{5}{ sqrt{x}}+x+1 } \ \ x+ frac{2}{ sqrt{x} }= -frac{5}{ sqrt{x}}+x+1 \ \ frac{2}{ sqrt{x} }+ frac{5}{ sqrt{x} }+x-x=1 \ \ frac{2+5}{ sqrt{x} }=1 \ \ frac{7}{ sqrt{x} }=1 \ \ sqrt{x} =7 \ x=49](https://tex.z-dn.net/?f=%28+frac%7B14%7D%7B23%7D%29%5E%7Bx%2B+frac%7B2%7D%7B+sqrt%7Bx%7D%7D+%7D%3D%28+frac%7B23%7D%7B14%7D+%29%5E%7B+frac%7B5%7D%7B+sqrt%7Bx%7D%7D-x-1+%7D+%5C++%5C+%28+frac%7B14%7D%7B23%7D%29%5E%7Bx%2B+frac%7B2%7D%7B+sqrt%7Bx%7D%7D+%7D%3D%28+frac%7B14%7D%7B23%7D+%29%5E%7B+-frac%7B5%7D%7B+sqrt%7Bx%7D%7D%2Bx%2B1+%7D++%5C++%5C+x%2B+frac%7B2%7D%7B+sqrt%7Bx%7D+%7D%3D+-frac%7B5%7D%7B+sqrt%7Bx%7D%7D%2Bx%2B1+%5C++%5C++frac%7B2%7D%7B+sqrt%7Bx%7D+%7D%2B+frac%7B5%7D%7B+sqrt%7Bx%7D+%7D%2Bx-x%3D1+%5C++%5C++frac%7B2%2B5%7D%7B+sqrt%7Bx%7D+%7D%3D1+%5C++%5C++frac%7B7%7D%7B+sqrt%7Bx%7D+%7D%3D1+%5C++%5C++sqrt%7Bx%7D+%3D7+%5C+x%3D49)
Ответ:![49 49](https://tex.z-dn.net/?f=49)
№2.
![2*3^{-2x+2}=3^{-x+1}+1 \ 2*3^{2(-x+1)}-3^{-x+1}-1=0 \ 3^{-x+1}=a \ 2a^2-a-1=0 \ D=1-4*2*(-1)=1+8=9 \ a_1= frac{1+3}{4}= frac{4}{4}=1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2= frac{1-3}{4}=- frac{2}{4}=- frac{1}{2} \ \ 3^{-x+1}=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3^{-x+1}=- frac{1}{2} \ -x+1=0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3^{-x+1} textgreater 0~~~~~= textgreater ~~~3^{-x+1} neq - frac{1}{2}\ x=1 2*3^{-2x+2}=3^{-x+1}+1 \ 2*3^{2(-x+1)}-3^{-x+1}-1=0 \ 3^{-x+1}=a \ 2a^2-a-1=0 \ D=1-4*2*(-1)=1+8=9 \ a_1= frac{1+3}{4}= frac{4}{4}=1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2= frac{1-3}{4}=- frac{2}{4}=- frac{1}{2} \ \ 3^{-x+1}=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3^{-x+1}=- frac{1}{2} \ -x+1=0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3^{-x+1} textgreater 0~~~~~= textgreater ~~~3^{-x+1} neq - frac{1}{2}\ x=1](https://tex.z-dn.net/?f=2%2A3%5E%7B-2x%2B2%7D%3D3%5E%7B-x%2B1%7D%2B1+%5C+2%2A3%5E%7B2%28-x%2B1%29%7D-3%5E%7B-x%2B1%7D-1%3D0+%5C++3%5E%7B-x%2B1%7D%3Da+%5C+2a%5E2-a-1%3D0+%5C+D%3D1-4%2A2%2A%28-1%29%3D1%2B8%3D9+%5C+a_1%3D+frac%7B1%2B3%7D%7B4%7D%3D+frac%7B4%7D%7B4%7D%3D1+%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7Ea_2%3D+frac%7B1-3%7D%7B4%7D%3D-+frac%7B2%7D%7B4%7D%3D-+frac%7B1%7D%7B2%7D+%5C++%5C+3%5E%7B-x%2B1%7D%3D1%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E3%5E%7B-x%2B1%7D%3D-+frac%7B1%7D%7B2%7D+%5C+-x%2B1%3D0+%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E3%5E%7B-x%2B1%7D+textgreater++0%7E%7E%7E%7E%7E%3D+textgreater++%7E%7E%7E3%5E%7B-x%2B1%7D+neq+-+frac%7B1%7D%7B2%7D%5C+x%3D1)
Ответ:![1 1](https://tex.z-dn.net/?f=1)
№4.
![2*4^x-5*6^x+3*9^x=0|~:9^x neq 0\ \ 2*frac{4^x}{9^x} -5* frac{6^x}{9^x}+3* frac{9^x}{9^x} =0 \ \ 2*( frac{4}{9})^x-5*( frac{6}{9} )^x+3=0 \ \ 2*( frac{2}{3})^{2x}-5*( frac{2}{3})^x+3=0 \ \ ( frac{2}{3})^x=a \ \ 2a^2-5a+3=0 \ D=25-4*2*3=25-24=1 \ a_1= frac{5+1}{4}= frac{6}{4}= frac{3}{2}~~~~~~~~~~~~~~~~~~~~~~a_2= frac{5-1}{4}= frac{4}{4}=1 \ \ ( frac{2}{3})^x= frac{3}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~( frac{2}{3})^x=1 \ \ x=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x=0 2*4^x-5*6^x+3*9^x=0|~:9^x neq 0\ \ 2*frac{4^x}{9^x} -5* frac{6^x}{9^x}+3* frac{9^x}{9^x} =0 \ \ 2*( frac{4}{9})^x-5*( frac{6}{9} )^x+3=0 \ \ 2*( frac{2}{3})^{2x}-5*( frac{2}{3})^x+3=0 \ \ ( frac{2}{3})^x=a \ \ 2a^2-5a+3=0 \ D=25-4*2*3=25-24=1 \ a_1= frac{5+1}{4}= frac{6}{4}= frac{3}{2}~~~~~~~~~~~~~~~~~~~~~~a_2= frac{5-1}{4}= frac{4}{4}=1 \ \ ( frac{2}{3})^x= frac{3}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~( frac{2}{3})^x=1 \ \ x=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x=0](https://tex.z-dn.net/?f=2%2A4%5Ex-5%2A6%5Ex%2B3%2A9%5Ex%3D0%7C%7E%3A9%5Ex+neq+0%5C++%5C++2%2Afrac%7B4%5Ex%7D%7B9%5Ex%7D+-5%2A+frac%7B6%5Ex%7D%7B9%5Ex%7D%2B3%2A+frac%7B9%5Ex%7D%7B9%5Ex%7D+%3D0+%5C++%5C+2%2A%28+frac%7B4%7D%7B9%7D%29%5Ex-5%2A%28+frac%7B6%7D%7B9%7D+%29%5Ex%2B3%3D0+%5C++%5C+2%2A%28+frac%7B2%7D%7B3%7D%29%5E%7B2x%7D-5%2A%28+frac%7B2%7D%7B3%7D%29%5Ex%2B3%3D0+%5C++%5C+%28+frac%7B2%7D%7B3%7D%29%5Ex%3Da+%5C++%5C+2a%5E2-5a%2B3%3D0+%5C+D%3D25-4%2A2%2A3%3D25-24%3D1+%5C+a_1%3D+frac%7B5%2B1%7D%7B4%7D%3D+frac%7B6%7D%7B4%7D%3D+frac%7B3%7D%7B2%7D%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7Ea_2%3D+frac%7B5-1%7D%7B4%7D%3D+frac%7B4%7D%7B4%7D%3D1++%5C+%5C+%28+frac%7B2%7D%7B3%7D%29%5Ex%3D+frac%7B3%7D%7B2%7D%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%28+frac%7B2%7D%7B3%7D%29%5Ex%3D1+%5C++%5C+x%3D-1%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7Ex%3D0)
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№2.
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№4.
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Спасибо большое:)
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