The solution set of the inequality 3log3√x−1<3log3(x−6)+3 is
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 B(6,∞) 3log3√x−1<3log3(x−6)+3
Clearly, x>6 ⇒√x−1<(x−6)+3 ⇒√x−1<x−3
Squaring both sides, we get (x−1)<(x−3)2 ⇒(x−1)<x2−6x+9 ⇒x2−7x+10>0 ⇒(x−5)(x−2)>0 ⇒x∈(−∞,2)∪(5,∞)
But x>6 ∴x∈(6,∞)