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Question

log(x2)(2x3)>log(x2)(246x)
The solution set of the above inequality has integral values of x ___

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Solution

278<x<4 and 2<x<3
We must have 2x3>0,246x>0
or x>32 and x<4
Also base x2>0x>2
Hence we must have x>2 and x<4(1)
Now if base x-2>1 i.e. x > 3, then we must have
2x3>246x
or 8x>27x>278(2)
Hence from (1) and (2), we have
278<x<4
However if 0<x2<1 or 2<x<3 then we
must have 2x3<246x or 8x<27x<278
In this case we have 2<x<3(B)
Both (A) and (B) give the required solution


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