The set of all values of x satisfying xlogx(1−x)2=9 is
a finite set
Taking algorithm of both the sides with base 3, we have
logx(1−x)2log3x=2⇒log3(1−x)2log3x log3x=2 ⇒log3(1−x)2=2 ⇒(1−x)2=9 (clearly x≠3) ⇒x=4,−2. But x>0 ⇒x=4