Given log2(x2+2x−1)=1 ⇒log2(x2+2x−1)=log22 ⇒x2+2x−1=2 ⇒x2+2x−3=0 ⇒x2+3x−x−3=0 ⇒x(x+3)−1(x+3)=0 ⇒x+3)(x−1)=0 ⇒x=1,−3 Since, x=1 and x=−3 are satisfy the given equation therefore the number of solutions of the equation are two.