1. log0,5 x<1 2. lg x<2 3. log1/3(5x-1)>-2 4. log5(3x-2)<2 5. log1/4(2x+1)>-1 6....

Question

1. log0,5 x<1<br> 2. lg x<2<br> 3. log1/3(5x-1)>-2
4. log5(3x-2)<2<br> 5. log1/4(2x+1)>-1
6. log1/3(3x+1)>log1/3(x+3)
7. log0,2 x< log0,2 (3x-6)
8. log4(2x-1)<(c линией)log4(x+3)<br> ПОМОГИТЕ!!!!!!!!!!!!!!!!!!!!!!

Answer 1

1) ОДЗ : Х>0
Log0,5 xОснование логарифма 0,5<1<br>Знак меняем
Х>0,5
2) ОДЗ: Х>0
Lg x<2Lg10<br> Lg x< Lg10^2
Lg x< Lg100
Основание логарифма 10>1 знак оставляем
Х<100<br>3)ОДЗ: 5х-1>0 Х>1/5
Log1/3 (5x-1)> -2
Log1/3(5x-1)> -2log1/3 1/3
Log1/3(5x-1)>log1/3 1/3^-2
Log1/3(5x-1)>log1/3 9
1/3<1 знак меняем<br>5х-1<9<br>5х<10<br>Х<2<br>\\\\\\\\\\\\\\\\\\\\\\
------(1/5)---------(2)--------
///////////////////////
Х€(1/5; 2)
4)ОДЗ: 3х-2>0
3х>2. Х>2/3
Log5 (3x-2)<2Log5 5<br>Log5 (3x-2)Log5(3x-2)Основание 5>1 знак оставляем
3х-2<25<br>3х<27<br>Х<9<br> \\\\\\\\\\\\\\\\\\\\\
-------(2/3)------(9)--------
///////////////////////
Х€(2/3; 9)


5.одз: 2х+1>0. 2х>-1
Х> -1/2
Log1/4(2x+1)> -1Log1/4 1/4
Log1/4(2x+1)>Log1/4 (1/4)^-1
Log1/4(2x+1)>Log1/4 4
1/4<1 знак меняем<br>2х+1<4<br>2х<3<br>Х<3/2<br>\\\\\\\\\\\\\\\\\\\\\\\
------(-1/2)--------(3/2)----
///////////////////////
Х€(-1/2; 3/2)

6. 3х+1>0. Х> -1/3
{Х+3>0. {Х> -3
/////////////////////////
----(-3)------(-1/3)----------
\\\\\\\\\\\\\\
Х> -1/3

3х+1 <Х+3<br>(Знак сменили те 1/3<1)<br>2х<2<br>Х<1<br>\\\\\\\\\\\\\\\\\\\\\\
-------(-1/3)-------(1)---------
//////////////////////
Х€(-1/3; 1)
Попробуй это просто!
Не получится пиши, доделаю!