The values of x satisfying xlog5x>5 lie in the interval
A
(0,∞)
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B
(0,15)∪(5,∞)
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C
(1,∞)
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D
(1,2)
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Solution
The correct option is B(0,15)∪(5,∞) We have, xlog5x>5 Clearly, it is meaningful for x>0.
Now, two cases arise: Case 1: When x>1 In this case, we have xlog5x>5 ⇒log5x>logx5[∵ax>N⇒x>logaNifa>1] ⇒log5x>1log5x ⇒(log5x−1)(log5x+1)>0 ⇒log5x−1>0⇒x>5⇒x∈(5,∞)