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Question

The solution set of inequality log5(x3)+12log53<12log5(2x26x+7) is

A
(2,10)
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B
(3,10)
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C
(3,)
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D
(4,10)
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Solution

The correct option is B (3,10)
log5(x3)+12log53<12log5(2x26x+7)
log function is defined when
(i) x>3
(ii) 2x26x+7>0
As D<0, so 2x26x+7>0 xR

Now, 2log5(x3)+log53<log5(2x26x+7)
log53(x3)2<log5(2x26x+7)
3(x3)2<(2x26x+7)
3x218x+27<2x26x+7
x212x+20<0
(x2)(x10)<0
x(2,10) ...(iii)

From (i),(ii) and (iii), we get
x(3,10)

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