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Question

The integral value of x satisfying the equation log3x2|log3x2|=2, is

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Solution

Clearly, x>0
log3x2|log3x2|=2
|2log3x2||log3x2|=2
Let log3x=t
Then, 2|t1||t2|=2

Case 1: t2
2(t1)(t2)=2
t=2
x=9

Case 2: 1<t<2
2(t1)+(t2)=2
t=2 Not possible

Case 3: t1
2(t1)+(t2)=2
t=2
x=19

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