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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: log inequalities
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umang (229)

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Hey !
I solved this question , but was getting a slightly different answer . Pls check -
Solve for all values of x :
logx(2x-3/4) > 2 .
 
Dont forget to take all cases !!!!!

Umang
    
shreyasnivas (256)

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1/2 and 3/2?
and what cases r u saying.. maybe i left loads out..
constraints: x is greater than zero, greater than 3/8,x cannot = 1, 0.
what else?
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fused_bulb (233)

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x has to be positive...( 3/8 , infinity ) - { 1 }...base cant be 1...

so...x^2 - 2x + 3/4 < 0

implies... x belongs to ( 1/3 , 1/2 )...

therefore....the reqd values of x are .....( 3/8 , 1/2 )....ANS

n dont 4gt 2 rate me...

............tseb eht ma i
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umang (229)

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just combine all ur results and form one result
The answer is x belongs to ( 3/8 , 1/2 ) union ( 1, 3/2)

Umang
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him26.89 (207)

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case 1)      x>1
 2x - 3/4 >x2
(2x-3)(2x-1)<0
x (1/2,3/2)
 
but acc to case ans for case is
x  (1,3/2)
 
case 2)     0<x<1
(2x-3)(2x-1) >0
 x  (-,1/2)  (3/2,)
 
acc. to case ans is (0,1/2)
 
net result is
x  (0,1/2)(1,3/2)
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umang (229)

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Hey him26.89 ,
i hav already posted the answer . All r getting it different

Umang
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umang (229)

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Hey him !
u left one case , and thats 2x-3/4>0 .
here u get x>3/8 . Just combine and u get the correct answer .
Thank u all for contributing !!!!!

Umang
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shreyasnivas (256)

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hey you are sharp him2689!! good job
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