у=10 это прямая параллельная оси Ох, при любом значении х, значение у всегда равно 10
1) log₆108*12-log₆6=log₆6⁴-1=4-1=3;
2) log₂(1/√2)-log₂(1/√2)=log₂(1/√2:1/√2)=log₂1=0;
3) ![\frac{(log_510-log_52)(log_510+log_52)}{log_320}=log_55log_520:\frac{log_520}{log_53}=log_53](https://tex.z-dn.net/?f=%5Cfrac%7B%28log_510-log_52%29%28log_510%2Blog_52%29%7D%7Blog_320%7D%3Dlog_55log_520%3A%5Cfrac%7Blog_520%7D%7Blog_53%7D%3Dlog_53)
4)![4^{0,5}*4^{-log_25}-log_3(\frac{1}{3}*log_55)=2*(\frac{1}{2^{log_25}})^2-log_33^{-1}=2*(\frac{1}{5})^2+log_33=\frac{2}{25}+1=1\frac{2}{25}](https://tex.z-dn.net/?f=4%5E%7B0%2C5%7D%2A4%5E%7B-log_25%7D-log_3%28%5Cfrac%7B1%7D%7B3%7D%2Alog_55%29%3D2%2A%28%5Cfrac%7B1%7D%7B2%5E%7Blog_25%7D%7D%29%5E2-log_33%5E%7B-1%7D%3D2%2A%28%5Cfrac%7B1%7D%7B5%7D%29%5E2%2Blog_33%3D%5Cfrac%7B2%7D%7B25%7D%2B1%3D1%5Cfrac%7B2%7D%7B25%7D)
5)![lg5*(lg10+lg2)+lg^22=lg5*(1+lg2)+lg^22=lg5+lg2*lg5+lg^22=lg5+lg2(lg5+lg2)=lg5+lg2(lg10)=lg5+lg2=lg10=1](https://tex.z-dn.net/?f=lg5%2A%28lg10%2Blg2%29%2Blg%5E22%3Dlg5%2A%281%2Blg2%29%2Blg%5E22%3Dlg5%2Blg2%2Alg5%2Blg%5E22%3Dlg5%2Blg2%28lg5%2Blg2%29%3Dlg5%2Blg2%28lg10%29%3Dlg5%2Blg2%3Dlg10%3D1)
6)![log_{5^{0,5}}2^2log_{7^2}5*log_{2^3}7=\frac{2}{0,5*2*3}log_52log_75*log_27=\frac{2}{3}\frac{lg2}{lg5}\frac{lg5}{lg7}\frac{lg7}{lg2}=\frac{2}{3}](https://tex.z-dn.net/?f=log_%7B5%5E%7B0%2C5%7D%7D2%5E2log_%7B7%5E2%7D5%2Alog_%7B2%5E3%7D7%3D%5Cfrac%7B2%7D%7B0%2C5%2A2%2A3%7Dlog_52log_75%2Alog_27%3D%5Cfrac%7B2%7D%7B3%7D%5Cfrac%7Blg2%7D%7Blg5%7D%5Cfrac%7Blg5%7D%7Blg7%7D%5Cfrac%7Blg7%7D%7Blg2%7D%3D%5Cfrac%7B2%7D%7B3%7D)
На 2 случая:
1)2х-5>0,2х=10,х= 5
2)2х-5<0,5-2х+3-8=9,х=0
![\frac{3x-1}{6} - \frac{x}{3} = \frac{5-x}{9}](https://tex.z-dn.net/?f=+%5Cfrac%7B3x-1%7D%7B6%7D+-+%5Cfrac%7Bx%7D%7B3%7D+%3D+%5Cfrac%7B5-x%7D%7B9%7D+)
Приведем к общему знаменателю:
![\frac{3*(3x-1)}{3*6} - \frac{6*x}{6*3} = \frac{2*(5-x)}{2*9}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2A%283x-1%29%7D%7B3%2A6%7D+-+%5Cfrac%7B6%2Ax%7D%7B6%2A3%7D+%3D+%5Cfrac%7B2%2A%285-x%29%7D%7B2%2A9%7D)
Избавимся от знаменателя ( умножим на 18):
3(3х-1) - 6х = 2 *(5-х)
9х-3-6х=10-2х
3х-3=10-2х
3х+2х=10+3
х=13/5 =2,6
Проверим:
![\frac{3*2,6-1}{6} - \frac{2,6}{3} = \frac{5-2,6}{9} \\ \\ \frac{6,8}{6} - \frac{2,6}{3} = \frac{2,4}{9} \\ \\ ](https://tex.z-dn.net/?f=%5Cfrac%7B3%2A2%2C6-1%7D%7B6%7D+-+%5Cfrac%7B2%2C6%7D%7B3%7D+%3D+%5Cfrac%7B5-2%2C6%7D%7B9%7D+%5C%5C++%5C%5C++%5Cfrac%7B6%2C8%7D%7B6%7D+-+%5Cfrac%7B2%2C6%7D%7B3%7D+%3D+%5Cfrac%7B2%2C4%7D%7B9%7D++%5C%5C++%5C%5C++%0A)
![\frac{20,4 -15,6}{18} = \frac{4,8}{18} \\ \\ \frac{4,8}{18} = \frac{4,8}{18} ](https://tex.z-dn.net/?f=%5Cfrac%7B20%2C4+-15%2C6%7D%7B18%7D+%3D+%5Cfrac%7B4%2C8%7D%7B18%7D++%5C%5C++%5C%5C++%5Cfrac%7B4%2C8%7D%7B18%7D+%3D+%5Cfrac%7B4%2C8%7D%7B18%7D+%0A)