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Question

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


A

x(3,π)(π,3π2)(3π2,5)

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B

x(3,π)(π,5)

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C

x(3,5π2)

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D

None of these.

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Solution

The correct option is A

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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