The number of solution of log 5+log (x2+1)log (x-2)=2 is

We have log 5+log (x2+1)log (x-2)=2⇒log {5(x2+1)}=log (x-2)2⇒5(x2+1)=(x-2)2  ⇒4x2+4x+1=0⇒x=-12Bur for x=-12log (x-2) is not meaningful.Hence it has no root.