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)
Cosa=-√1-5/9=-√4/9=-2/3
3cosa-2=3*(-2/3)-2=-2-2=-4
3 sin x + 5 cos y =5
4 sin x - cos y = -1 умножаем второе уравнение на 5 и складываем с первым
23 sin x = 0
x = Pi n
cos y =1
y = 2 Pi n
Ответ:
сумма x и у меньше чем -2
вариант в