If a > 0 and Limx→aax−xaxx−aa=−1   then a =

Limit value is 0/0 ,Use L-Hospital rule ddx(ax)=axloga,ddx(xa)=a.xa−1ddx(xx)=xx(1+logx)limx→a  axloga-axa-1xx(1+logx)-0=aaloga-aaaa(1+loga)=-1loga-1=-1-loga2loga=0a=1