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Question

balog xxdx=

A
log(log blog a)
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B
log(ab)log(ba)
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C
12log(ab)log(ba)
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D
12log(ab)log(ab)
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Solution

The correct option is C 12log(ab)log(ba)
Let I=ba1xlog x dx=(log x log x)baba1xlog x dx
2I=[(log x)2]baI=12[(log b)2(log a)2]
12[(log b+log a)(log blog a)]=12log(ab)log(ba)

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