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)
Вправо - значит от начала координат, тогда: 396
1,2х-0,2=1,5х+ 0,2 х + 0,2
1,2 х -0,2х-1,5х=0,2+0,2
-0,5х=0,4
х= 0,4: (-0,5)
х=-0,8
1.
ОДЗ: π-x≠0 x/(π-x)≥0
x≠π x(π-x)≥0
x=0 x=π
- + -
-------- 0 ------------ π ---------
\\\\\\\\\\\\\\\\
x∈[0; π)
a) x/(π-x) =0
x=0
б) 2sinx-1=0
2sinx=1
sinx=1/2
x=(-1)ⁿ (π/6) + πn, n∈Z
С учетом ОДЗ:
при х=0 х=(-1)⁰ (π/6) + π*0= π/6
при х=1 х=(-1)¹ (π/6) + π*1= - (π/6) + π = 5π/6
Ответ: 0; π/6; 5π/6.
2.
ОДЗ: х≠4
(a-3)x²+5x-2=0
Уравнение имеет единственное значение при D=0.
D=5²-4(a-3)*(-2)=25+8(a-3)=25+8a-24=8a+1
8a+1=0
8a= -1
a= - 1/8
a= - 0.125
Ответ: -0,125.