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Question

If log|sinx|(x28x+23)>3log2|sinx|


  1. None of these.

  2. x(3,5π2)

  3. x(3,π)(π,5)

  4. x(3,π)(π,3π2)(3π2,5)


Solution

The correct option is D

x(3,π)(π,3π2)(3π2,5)


The given inequality can be written as log2(x28x+23)log2|sinx|>3log2|sinx|

As |sinx| can only take values 0<|sinx|<1 the value of 
log2|sinx| is negative.

log2(x28x+23)<3x28x+23<23=8x28x+15<0(x5)(x3)<03<x<5

But the terms in the inequality are meaningful if |sinx|0, 1
So, /nπ2.
Hence x(3,π)(π,3π2)(3π2,5).
 

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