Помогите пожалуйста решить 4 и 5 задания

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Дано ответов: 2

Правильный ответ

$\frac{5}{|3-\log_{0,5}x|+4}-|3-\log_{0,5}x|\textgreater0, \\ |3-\log_{0,5}x|=t, \ t \geq 0, \\ \frac{5}{t+4}-t\textgreater0, \\ \frac{5-t(t+4)}{t+4}\textgreater0, \\ \frac{-t^2-4t+5}{t+4}\textgreater0, \\ -t^2-4t+5=0, \\ t^2+4t-5=0, \\ t_1=-5, t_2=1, \\ -t^2-4t+5=-(t+5)(t-1), \\ -(t+5)(t-1)(t+4)\textgreater0, \\ (t+5)(t-1)(t+4)\textless0, \\ t\in(-\infty;-5)\cup(-4;1), \\ 0\leq t\textless1; \\ 0\leq|3-\log_{0,5}x|\textless1, \\ -1\textless3-\log_{0,5}x\textless1, \\ -4\textless-\log_{0,5}x\textless-2,$
$2\textless\log_{0,5}x\textless4, \\ 0,5\ \textless \ 1, \\ 0,5^4\ \textless \ x\ \textless \ 0,5^2, \\ \frac{1}{16}\ \textless \ x\ \textless \ \frac{1}{4}, \\ x\in( \frac{1}{16}; \frac{1}{4}).$

" alt="162\cdot3^{5-x}-2\cdot3^{x-5}\ \textgreater \ 0, \\ 3^{x-5}(81\cdot(\frac{1}{9})^{x-5}-1)\ \textgreater \ 0, \\ \left [ {{ \left \{ {{3^{x-5}\ \textgreater \ 0,} \atop {(\frac{1}{9})^{x-5}\ \textgreater \ \frac{1}{81};}} \right. } \atop { \left \{ {{3^{x-5}\ \textless \ 0,} \atop {(\frac{1}{9})^{x-5}\ \textless \ \frac{1}{81};}} \right. }} \right. \left [ {{ \left \{ {{x\in R,} \atop {x-5\ \textless \ 2;}} \right. } \atop { \left \{ {{x\in\varnothing,} \atop {x-5\ \textgreater \ 2;}} \right. }} \right. \left [ {{x\ \textless \ 7,} \atop {x\in\varnothing;}} \right. \\ x\ \textless \ 7. \\ \max x 6." align="absmiddle" class="latex-formula">

arsenlevadniy_zn (93.5k баллов) 29 Апр, 18

sedinalana_zn · Answer 1 · 2018-04-29T14:56:50+0000

4
ОДЗ x>0
|3-log(0,5)x|=a
5/(a+4)-a>0
(5-a²-4a)/(a+4)>0
(a²+4a-5)/(a+4)<0 a²+4a-5=0⇒a1=a2=-4 U a1*a2=-5⇒a1=-5 U a2=1
a+4=0⇒a=-4
_ + _ +
---------------(-5)-----------(-4)---------------(1)--------------------------
a<-5⇒|3-log(0,5)x|<-5 нет решения -4<|3-log(0,5)x|<1⇒|3-log(0,5)x|<1 -1<3-log(0,5)x<1 -4<-log(0,5)x<-2 2основание меньше 1 знак меняется
1/16БчБ1/4
Jndtn ч∈(1/16ж1/4)
5
3^(x-5)=a
162/a-2a>0
(162-2a²)/a>0
2(a²-81)/a<0 a²-81=0
a2=81
a=-9
a=9
a=0
_ + _ +
---------------------(-9)-----------(0)------------------(9)-----------------
a<-9⇒3^(x-5)<-9 нет решения 0x-5<2 x<7 Ответ x∈(-∞;7),х=6-наиб