1)
![log_{3} \frac{3x-5}{x+1} \leq 1](https://tex.z-dn.net/?f=log_%7B3%7D+%5Cfrac%7B3x-5%7D%7Bx%2B1%7D+%5Cleq+1+)
ОДЗ:
![\frac{3x-5}{x+1} \ \textgreater \ 0](https://tex.z-dn.net/?f=+%5Cfrac%7B3x-5%7D%7Bx%2B1%7D+%5C+%5Ctextgreater+%5C+0)
--------+--------(-1)---- - ------(5/3)------+----------
///////////////////// //////////////////////
![x](https://tex.z-dn.net/?f=x)
∈
![(-](https://tex.z-dn.net/?f=%28-)
∞
![;-1)](https://tex.z-dn.net/?f=%3B-1%29)
∪
![(1 \frac{2}{3} ;+](https://tex.z-dn.net/?f=%281+%5Cfrac%7B2%7D%7B3%7D+%3B%2B)
∞
![)](https://tex.z-dn.net/?f=%29)
![log_{3} \frac{3x-5}{x+1} \leq log_{3} 3](https://tex.z-dn.net/?f=log_%7B3%7D+%5Cfrac%7B3x-5%7D%7Bx%2B1%7D+%5Cleq+log_%7B3%7D+3)
![\frac{3x-5}{x+1} \leq 3](https://tex.z-dn.net/?f=%5Cfrac%7B3x-5%7D%7Bx%2B1%7D+%5Cleq+3)
![\frac{3x-5}{x+1} -3 \leq 0](https://tex.z-dn.net/?f=%5Cfrac%7B3x-5%7D%7Bx%2B1%7D+-3+%5Cleq+0)
![\frac{3x-5-3x-3}{x+1} \leq 0](https://tex.z-dn.net/?f=%5Cfrac%7B3x-5-3x-3%7D%7Bx%2B1%7D+%5Cleq+0)
![\frac{-8}{x+1} \leq 0](https://tex.z-dn.net/?f=%5Cfrac%7B-8%7D%7Bx%2B1%7D+%5Cleq+0)
![\frac{8}{x+1} \geq 0](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7Bx%2B1%7D+%5Cgeq+0)
![x+1\ \textgreater \ 0](https://tex.z-dn.net/?f=x%2B1%5C+%5Ctextgreater+%5C+0)
![x\ \textgreater \ -1](https://tex.z-dn.net/?f=x%5C+%5Ctextgreater+%5C+-1)
-----------(-1)-------------------------
////////////////////////
-----------(-1)-------(5/3)------------
//////////// /////////////
Ответ:
![(1 \frac{2}{3} ;+](https://tex.z-dn.net/?f=%281+%5Cfrac%7B2%7D%7B3%7D+%3B%2B)
∞
![)](https://tex.z-dn.net/?f=%29)
2)
![(5x-2)*log_ \frac{1}{3}x\ \textless \ 0](https://tex.z-dn.net/?f=%285x-2%29%2Alog_+%5Cfrac%7B1%7D%7B3%7Dx%5C+%5Ctextless+%5C+0+)
ОДЗ:
![x\ \textgreater \ 0](https://tex.z-dn.net/?f=x%5C+%5Ctextgreater+%5C+0)
![-(5x-2)*log_ 3}x\ \textless \ 0](https://tex.z-dn.net/?f=-%285x-2%29%2Alog_+3%7Dx%5C+%5Ctextless+%5C+0+)
![(5x-2)*log_ 3}x\ \textgreater \ 0](https://tex.z-dn.net/?f=%285x-2%29%2Alog_+3%7Dx%5C+%5Ctextgreater+%5C+0+)
![log_ 3}x=0](https://tex.z-dn.net/?f=log_+3%7Dx%3D0)
![x=1](https://tex.z-dn.net/?f=x%3D1)
-------+-------(0.4)------ - ------(1)----------+--------
//////////////////// ////////////////////
--------(0)------------------------------------------------
/////////////////////////////////////////////////
Ответ: (0; 0.4) ∪ (1; + ∞ )