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los88
@los88
December 2021
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(log_x 2 -1)log_2 2x<1,5
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MizoriesKun
(㏒ₓ2 -1)*㏒₂2х <1,5 ОДЗ х>0
1
( ------- - 1 ) *㏒₂2х <1,5
㏒₂х
㏒₂2х - ㏒₂2х* ㏒₂х <1,5*㏒₂х
㏒₂2+㏒₂х -(㏒₂2+㏒₂х)*㏒₂х <1,5*㏒₂х
1+㏒₂х- ㏒₂х-㏒²₂х <1,5*㏒₂х
㏒²₂х +1,5*㏒₂х-1 >0
замена ㏒₂х= а
а²+1,5а-1=0
D=2,25+4=6,25 √D=2,5
a=(-1,5+2,5)/2=1/2 ㏒₂х=1/2 x=√2
a=(-1,5-2,5)/2=-2 ㏒₂х=-2 x=1/4
- + -
-0-----1/4------------√2---------
x∈(0;1/4)∪(√2; +∞)
2 votes
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Answers & Comments
1
( ------- - 1 ) *㏒₂2х <1,5
㏒₂х
㏒₂2х - ㏒₂2х* ㏒₂х <1,5*㏒₂х
㏒₂2+㏒₂х -(㏒₂2+㏒₂х)*㏒₂х <1,5*㏒₂х
1+㏒₂х- ㏒₂х-㏒²₂х <1,5*㏒₂х
㏒²₂х +1,5*㏒₂х-1 >0
замена ㏒₂х= а
а²+1,5а-1=0
D=2,25+4=6,25 √D=2,5
a=(-1,5+2,5)/2=1/2 ㏒₂х=1/2 x=√2
a=(-1,5-2,5)/2=-2 ㏒₂х=-2 x=1/4
- + -
-0-----1/4------------√2---------
x∈(0;1/4)∪(√2; +∞)