Предмет: Алгебра,
автор: aiserdaiza
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Автор ответа:
0
176.
![1) 5^{x-3}- 5^{x-4}=16* 5^{x-5}+4; \ 5^{x-5}( 5^{2}- 5-16)=4; \ 5^{x-5}*4=4; \ 5^{x-5}=1; \ 5^{x-5}= 5^{0}; \ x-5=0; \ x=5. \](https://tex.z-dn.net/?f=1%29+5%5E%7Bx-3%7D-+5%5E%7Bx-4%7D%3D16%2A+5%5E%7Bx-5%7D%2B4%3B+%5C++5%5E%7Bx-5%7D%28+5%5E%7B2%7D-+5-16%29%3D4%3B+%5C++5%5E%7Bx-5%7D%2A4%3D4%3B+%5C+5%5E%7Bx-5%7D%3D1%3B+%5C++5%5E%7Bx-5%7D%3D+5%5E%7B0%7D%3B+%5C+x-5%3D0%3B+%5C+x%3D5.++%5C+++++++++++ "1) 5^{x-3}- 5^{x-4}=16* 5^{x-5}+4; \ 5^{x-5}( 5^{2}- 5-16)=4; \ 5^{x-5}*4=4; \ 5^{x-5}=1; \ 5^{x-5}= 5^{0}; \ x-5=0; \ x=5. \")
Ответ: 5.
![2) 4^{x}- 3^{x-0,5}= 3^{x+0,5}- 2^{2x-1}; \ 2^{2x}+ 2^{2x-1}= 3^{x-0,5}+3^{x+0,5}; \ 2^{2x-1}(2+1)= 3^{x-0,5}( 1+3); \ 2^{2x-1}*3= 3^{x-0,5}*4; \ frac{ 2^{2x-1} }{ 2^{2} }= frac{ 3^{x-0,5} }{3}; \ 2^{2x-3}= 3^{x-1,5}; \ 2x-3=0; \ x=1,5; \ x-1,5=0; \ x=1,5. \](https://tex.z-dn.net/?f=2%29+4%5E%7Bx%7D-+3%5E%7Bx-0%2C5%7D%3D+3%5E%7Bx%2B0%2C5%7D-+2%5E%7B2x-1%7D%3B+%5C++2%5E%7B2x%7D%2B+2%5E%7B2x-1%7D%3D+3%5E%7Bx-0%2C5%7D%2B3%5E%7Bx%2B0%2C5%7D%3B+%5C++2%5E%7B2x-1%7D%282%2B1%29%3D+3%5E%7Bx-0%2C5%7D%28+1%2B3%29%3B+%5C++2%5E%7B2x-1%7D%2A3%3D+3%5E%7Bx-0%2C5%7D%2A4%3B+%5C++frac%7B+2%5E%7B2x-1%7D+%7D%7B+2%5E%7B2%7D+%7D%3D+frac%7B+3%5E%7Bx-0%2C5%7D+%7D%7B3%7D%3B+%5C++2%5E%7B2x-3%7D%3D+3%5E%7Bx-1%2C5%7D%3B+%5C+2x-3%3D0%3B+%5C+x%3D1%2C5%3B+%5C+x-1%2C5%3D0%3B+%5C+x%3D1%2C5.+%5C++++++++++++++++ "2) 4^{x}- 3^{x-0,5}= 3^{x+0,5}- 2^{2x-1}; \ 2^{2x}+ 2^{2x-1}= 3^{x-0,5}+3^{x+0,5}; \ 2^{2x-1}(2+1)= 3^{x-0,5}( 1+3); \ 2^{2x-1}*3= 3^{x-0,5}*4; \ frac{ 2^{2x-1} }{ 2^{2} }= frac{ 3^{x-0,5} }{3}; \ 2^{2x-3}= 3^{x-1,5}; \ 2x-3=0; \ x=1,5; \ x-1,5=0; \ x=1,5. \")
Ответ: 1,5.
![3) 2^{ x^{2} -1}- 3^{ x^{2} }= 3^{ x^{2} -1}- 2^{ x^{2} +2}; \ 2^{ x^{2} -1}+ 2^{ x^{2} +2}= 3^{ x^{2} -1}+ 3^{ x^{2} }; \ 2^{ x^{2} -1}(1+ 2^{3})= 3^{ x^{2} -1}(1+3); \ 2^{ x^{2} -1}*9= 3^{ x^{2} -1}*4; \ ( frac{2}{3}) ^{ x^{2} -1}= (frac{2}{3}) ^{2}; \ x^{2} -1=2; \ x^{2} =3; \ x=+- sqrt{3}. \](https://tex.z-dn.net/?f=3%29+2%5E%7B+x%5E%7B2%7D+-1%7D-+3%5E%7B+x%5E%7B2%7D+%7D%3D+3%5E%7B+x%5E%7B2%7D+-1%7D-+2%5E%7B+x%5E%7B2%7D+%2B2%7D%3B+%5C++2%5E%7B+x%5E%7B2%7D+-1%7D%2B+2%5E%7B+x%5E%7B2%7D+%2B2%7D%3D+3%5E%7B+x%5E%7B2%7D+-1%7D%2B+3%5E%7B+x%5E%7B2%7D+%7D%3B+%5C++2%5E%7B+x%5E%7B2%7D+-1%7D%281%2B+2%5E%7B3%7D%29%3D+3%5E%7B+x%5E%7B2%7D+-1%7D%281%2B3%29%3B+%5C++2%5E%7B+x%5E%7B2%7D+-1%7D%2A9%3D+3%5E%7B+x%5E%7B2%7D+-1%7D%2A4%3B+%5C+%28+frac%7B2%7D%7B3%7D%29+%5E%7B+x%5E%7B2%7D+-1%7D%3D+%28frac%7B2%7D%7B3%7D%29+%5E%7B2%7D%3B+%5C++x%5E%7B2%7D+-1%3D2%3B+%5C++x%5E%7B2%7D+%3D3%3B+%5C+x%3D%2B-+sqrt%7B3%7D.+%5C++++++++++++++++++ "3) 2^{ x^{2} -1}- 3^{ x^{2} }= 3^{ x^{2} -1}- 2^{ x^{2} +2}; \ 2^{ x^{2} -1}+ 2^{ x^{2} +2}= 3^{ x^{2} -1}+ 3^{ x^{2} }; \ 2^{ x^{2} -1}(1+ 2^{3})= 3^{ x^{2} -1}(1+3); \ 2^{ x^{2} -1}*9= 3^{ x^{2} -1}*4; \ ( frac{2}{3}) ^{ x^{2} -1}= (frac{2}{3}) ^{2}; \ x^{2} -1=2; \ x^{2} =3; \ x=+- sqrt{3}. \")
Ответ: +-√3.
![4) 5^{2x}- 7^{x}-35* 5^{2x}+35* 7^{x}=0; \ 5^{2x}-35* 5^{2x}= 7^{x}-35* 7^{x}; \ 5^{2x}(1-35)= 7^{x}(1-35); \ 5^{2x}= 7^{x}; \ x=0. \](https://tex.z-dn.net/?f=4%29+5%5E%7B2x%7D-+7%5E%7Bx%7D-35%2A+5%5E%7B2x%7D%2B35%2A+7%5E%7Bx%7D%3D0%3B+%5C++5%5E%7B2x%7D-35%2A+5%5E%7B2x%7D%3D+7%5E%7Bx%7D-35%2A+7%5E%7Bx%7D%3B+%5C++5%5E%7B2x%7D%281-35%29%3D+7%5E%7Bx%7D%281-35%29%3B+%5C++5%5E%7B2x%7D%3D+7%5E%7Bx%7D%3B+%5C+x%3D0.+%5C+++++++++++++ "4) 5^{2x}- 7^{x}-35* 5^{2x}+35* 7^{x}=0; \ 5^{2x}-35* 5^{2x}= 7^{x}-35* 7^{x}; \ 5^{2x}(1-35)= 7^{x}(1-35); \ 5^{2x}= 7^{x}; \ x=0. \")
Ответ: 0.
177.
![1) x* 3^{x-1}+3* 3^{ sqrt{3}-x }= 3^{x}+x* 3^{ sqrt{3}-x }; \ 3*3^{ sqrt{3}-x }-x* 3^{ sqrt{3}-x }= 3^{x}-x* 3^{x-1}; \ 3^{ sqrt{3}-x }(3-x)=3^{x-1}(3-x); \ 3^{ sqrt{3}-x }= 3^{x-1}; \ sqrt{3}-x=x-1; \ 2x=1+ sqrt{3}; \ x= frac{1+ sqrt{3} }{2}. \](https://tex.z-dn.net/?f=1%29+x%2A+3%5E%7Bx-1%7D%2B3%2A+3%5E%7B+sqrt%7B3%7D-x+%7D%3D+3%5E%7Bx%7D%2Bx%2A+3%5E%7B+sqrt%7B3%7D-x+%7D%3B+%5C+3%2A3%5E%7B+sqrt%7B3%7D-x+%7D-x%2A+3%5E%7B+sqrt%7B3%7D-x+%7D%3D+3%5E%7Bx%7D-x%2A+3%5E%7Bx-1%7D%3B+%5C++3%5E%7B+sqrt%7B3%7D-x+%7D%283-x%29%3D3%5E%7Bx-1%7D%283-x%29%3B+%5C+3%5E%7B+sqrt%7B3%7D-x+%7D%3D+3%5E%7Bx-1%7D%3B+%5C++sqrt%7B3%7D-x%3Dx-1%3B+%5C+2x%3D1%2B+sqrt%7B3%7D%3B+%5C+x%3D+frac%7B1%2B+sqrt%7B3%7D+%7D%7B2%7D.+%5C+++++++++++++++++++ "1) x* 3^{x-1}+3* 3^{ sqrt{3}-x }= 3^{x}+x* 3^{ sqrt{3}-x }; \ 3*3^{ sqrt{3}-x }-x* 3^{ sqrt{3}-x }= 3^{x}-x* 3^{x-1}; \ 3^{ sqrt{3}-x }(3-x)=3^{x-1}(3-x); \ 3^{ sqrt{3}-x }= 3^{x-1}; \ sqrt{3}-x=x-1; \ 2x=1+ sqrt{3}; \ x= frac{1+ sqrt{3} }{2}. \")
Ответ: (1+√3)/2; 3.
![2) x^{2} * 4^{ sqrt{6-x} }=16* 4^{ sqrt{6-x} }; \ x^{2} =16; \ x=+-4. \](https://tex.z-dn.net/?f=2%29+x%5E%7B2%7D+%2A+4%5E%7B+sqrt%7B6-x%7D+%7D%3D16%2A+4%5E%7B+sqrt%7B6-x%7D+%7D%3B+%5C++x%5E%7B2%7D+%3D16%3B+%5C+x%3D%2B-4.+%5C+++ "2) x^{2} * 4^{ sqrt{6-x} }=16* 4^{ sqrt{6-x} }; \ x^{2} =16; \ x=+-4. \")
Ответ: +-4.
Ответ: 5.
Ответ: 1,5.
Ответ: +-√3.
Ответ: 0.
177.
Ответ: (1+√3)/2; 3.
Ответ: +-4.
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