Giải các bất phương trình :
1)log3(x22)<log3(32|x|1)2)log12(4x)2>log12(6|x|3)3)log4(x25)<log4(73|x|3)4)log13(3x2)>log13(4|x|2)
1)
Điều kiện: {x22>032|x|1>0.
Khi đó ta có:
log3(x22)<log3(32|x|1){x22<32|x|1x22>0{2x23|x|2<0|x|>22<|x|<2[2<x<22<x<2(TM).
Vậy BPT đã cho có nghiệm [2<x<22<x<2.

2)  
Điều kiện: {4x06|x|3>0.
Khi đó ta có:
log12(4x)2>log12(6|x|3)
0<(4x)2<6|x|3
|x|28x+166|x|+3<0
[{x>0x214x+19<0{x<0x22x+19<0[{x>07302<x<7+302{x<0(x1)2+18<0(L)
Kết hợp với điều kiện vậy nghiệm cần tìm là
{7302<x<7+302x4

3)  
Điều kiện: {x25>073|x|3>0
Khi đó ta có:
log4(x25)<log4(73|x|3){x25<73|x|3x25>0{3x27|x|6<0|x|>55<|x|<3[3<x<55<x<3(TM).
Vậy BPT đã cho có nghiệm [3<x<55<x<3.

4)  
Điều kiện: {3x2>04|x|2>0.
Khi đó ta có:
log13(3x2)>log13(4|x|2)
0<3x2<4|x|2
|x|2+4|x|5>0
[|x|>1|x|<5x<1x>1.
Kết hợp với điều kiện vậy nghiệm cần tìm là [3<x<11<x<3

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