Предмет: Алгебра,
автор: Drezden12
Очень срочно!
Помогите решить задания по алгебре 9 класс.
Приложения:
![](https://files.topotvet.com/i/bcf/bcf264139833f3eff003318cabf777c7.jpg)
Ответы
Автор ответа:
0
1) ![26^{26-x}=4 26^{26-x}=4](https://tex.z-dn.net/?f=26%5E%7B26-x%7D%3D4)
![26-x=log_{26}(4) 26-x=log_{26}(4)](https://tex.z-dn.net/?f=26-x%3Dlog_%7B26%7D%284%29)
![x=26-log_{26}(4) x=26-log_{26}(4)](https://tex.z-dn.net/?f=x%3D26-log_%7B26%7D%284%29)
2)![8=4^{ frac{1}{26x+1} } 8=4^{ frac{1}{26x+1} }](https://tex.z-dn.net/?f=8%3D4%5E%7B+frac%7B1%7D%7B26x%2B1%7D+%7D)
![frac{1}{26x+1}=log_4(8) frac{1}{26x+1}=log_4(8)](https://tex.z-dn.net/?f=+frac%7B1%7D%7B26x%2B1%7D%3Dlog_4%288%29+)
![26x+1= frac{1}{log_4(8)} =log_8(4) 26x+1= frac{1}{log_4(8)} =log_8(4)](https://tex.z-dn.net/?f=26x%2B1%3D+frac%7B1%7D%7Blog_4%288%29%7D+%3Dlog_8%284%29)
![x= frac{log_8(4)-1}{26} x= frac{log_8(4)-1}{26}](https://tex.z-dn.net/?f=x%3D+frac%7Blog_8%284%29-1%7D%7B26%7D+)
3)![( frac{12}{41} )^{ frac{x}{26} +1}=( frac{51}{41} )^{ frac{x}{26} +1} ( frac{12}{41} )^{ frac{x}{26} +1}=( frac{51}{41} )^{ frac{x}{26} +1}](https://tex.z-dn.net/?f=%28+frac%7B12%7D%7B41%7D+%29%5E%7B+frac%7Bx%7D%7B26%7D+%2B1%7D%3D%28+frac%7B51%7D%7B41%7D+%29%5E%7B+frac%7Bx%7D%7B26%7D+%2B1%7D)
![(frac{12}{41}:frac{51}{41})^{ frac{x}{26} +1}=1 (frac{12}{41}:frac{51}{41})^{ frac{x}{26} +1}=1](https://tex.z-dn.net/?f=%28frac%7B12%7D%7B41%7D%3Afrac%7B51%7D%7B41%7D%29%5E%7B+frac%7Bx%7D%7B26%7D+%2B1%7D%3D1)
![(frac{12}{51})^{frac{x}{26} +1}=1 (frac{12}{51})^{frac{x}{26} +1}=1](https://tex.z-dn.net/?f=%28frac%7B12%7D%7B51%7D%29%5E%7Bfrac%7Bx%7D%7B26%7D+%2B1%7D%3D1)
![frac{x}{26} +1=0 frac{x}{26} +1=0](https://tex.z-dn.net/?f=frac%7Bx%7D%7B26%7D+%2B1%3D0)
![x=- frac{1}{26} x=- frac{1}{26}](https://tex.z-dn.net/?f=x%3D-+frac%7B1%7D%7B26%7D+)
4)![14^{26x}-14^{26x-1}=13 14^{26x}-14^{26x-1}=13](https://tex.z-dn.net/?f=14%5E%7B26x%7D-14%5E%7B26x-1%7D%3D13)
![14^{26x}- frac{1}{14}*14^{26x}=14^{26x}* frac{13}{14} =13 14^{26x}- frac{1}{14}*14^{26x}=14^{26x}* frac{13}{14} =13](https://tex.z-dn.net/?f=14%5E%7B26x%7D-+frac%7B1%7D%7B14%7D%2A14%5E%7B26x%7D%3D14%5E%7B26x%7D%2A+frac%7B13%7D%7B14%7D+%3D13+)
![14^{26x}* frac{1}{14} =14^{26x-1}=1 14^{26x}* frac{1}{14} =14^{26x-1}=1](https://tex.z-dn.net/?f=14%5E%7B26x%7D%2A+frac%7B1%7D%7B14%7D+%3D14%5E%7B26x-1%7D%3D1)
![26x-1=0 26x-1=0](https://tex.z-dn.net/?f=26x-1%3D0)
![x= frac{1}{26} x= frac{1}{26}](https://tex.z-dn.net/?f=x%3D+frac%7B1%7D%7B26%7D+)
5)![( frac{7}{8} )^{ frac{x-1}{2} }= sqrt[26]{frac{8}{7}}=( frac{8}{7} )^{ frac{1}{26} } =( frac{7}{8} )^{- frac{1}{26} } ( frac{7}{8} )^{ frac{x-1}{2} }= sqrt[26]{frac{8}{7}}=( frac{8}{7} )^{ frac{1}{26} } =( frac{7}{8} )^{- frac{1}{26} }](https://tex.z-dn.net/?f=%28+frac%7B7%7D%7B8%7D+%29%5E%7B+frac%7Bx-1%7D%7B2%7D+%7D%3D++sqrt%5B26%5D%7Bfrac%7B8%7D%7B7%7D%7D%3D%28+frac%7B8%7D%7B7%7D+%29%5E%7B+frac%7B1%7D%7B26%7D+%7D+%3D%28+frac%7B7%7D%7B8%7D+%29%5E%7B-+frac%7B1%7D%7B26%7D+%7D)
![frac{x-1}{2}=- frac{1}{26} frac{x-1}{2}=- frac{1}{26}](https://tex.z-dn.net/?f=+frac%7Bx-1%7D%7B2%7D%3D-+frac%7B1%7D%7B26%7D++)
![x-1=- frac{2}{26} =- frac{1}{13} x-1=- frac{2}{26} =- frac{1}{13}](https://tex.z-dn.net/?f=x-1%3D-+frac%7B2%7D%7B26%7D+%3D-+frac%7B1%7D%7B13%7D+)
![x = 1 - frac{1}{13} = frac{12}{13} x = 1 - frac{1}{13} = frac{12}{13}](https://tex.z-dn.net/?f=x+%3D+1+-++frac%7B1%7D%7B13%7D+%3D+frac%7B12%7D%7B13%7D+)
6)![2^x+2^{x-3}=18 2^x+2^{x-3}=18](https://tex.z-dn.net/?f=2%5Ex%2B2%5E%7Bx-3%7D%3D18)
![2^x+ frac{1}{8}*2^x=2^x*(1+ frac{1}{8} ) =2^x* frac{9}{8} =18 2^x+ frac{1}{8}*2^x=2^x*(1+ frac{1}{8} ) =2^x* frac{9}{8} =18](https://tex.z-dn.net/?f=2%5Ex%2B+frac%7B1%7D%7B8%7D%2A2%5Ex%3D2%5Ex%2A%281%2B+frac%7B1%7D%7B8%7D+%29+%3D2%5Ex%2A+frac%7B9%7D%7B8%7D+%3D18)
![2^x* frac{1}{8} =2^{x-3}=2 2^x* frac{1}{8} =2^{x-3}=2](https://tex.z-dn.net/?f=2%5Ex%2A+frac%7B1%7D%7B8%7D+%3D2%5E%7Bx-3%7D%3D2)
x - 3 = 1
x = 4
7)![4^x - 6*2^x+8=0 4^x - 6*2^x+8=0](https://tex.z-dn.net/?f=4%5Ex+-+6%2A2%5Ex%2B8%3D0)
Замена 2^x = y > 0 при любом х
y^2 - 6y + 8 = 0
(y - 2)(y - 4) = 0
y1 = 2^x = 2; x1 = 1
y2 = 2^x = 4; x2 = 2
2)
3)
4)
5)
6)
x - 3 = 1
x = 4
7)
Замена 2^x = y > 0 при любом х
y^2 - 6y + 8 = 0
(y - 2)(y - 4) = 0
y1 = 2^x = 2; x1 = 1
y2 = 2^x = 4; x2 = 2
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