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Question

# Statement−1: If xlogx(3−x)2=25, then x=−2 Statement−2: alogax=x, if a>0, x>0 and a≠1.

A
Statement1 is true, Statement2 is true; Statement2 is a correct explanation for Statement1.
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B
Statement1 is true, Statement2 is true; Statement2 is NOT a correct explanation for Statement1.
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C
Statement1 is true, Statement2 is false.
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D
Statement1 is false, Statement2 is true.
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Solution

## The correct option is D Statement−1 is false, Statement−2 is true.xlogx(3−x)2=25 ⇒(3−x)2=25, x>0 and x≠1 [∵alogax=x] ⇒3−x=±5 ⇒x=−2, x=8 Hence, statement−2 is true but statement−1 is false.

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