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Question

Find the solution set of the given inequality:
3log3x1<3log3(x6)+3

A
(5,+)
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B
(6,+)
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C
(1,2)(3,5)
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D
(,2)(5,)
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Solution

The correct option is C (6,+)
3log3x1<3log3(x6)+3
x1log33<(x6)log33+3
x1<(x6)+3
x1<x3
Squaring both sides,
(x1)<(x3)2
x1<x26x+9
x27x+10>0(x5)(x2)>0
xϵ(,2)(5,)
But, x6>0x>6
xϵ(6,)

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