Let $ f$ be a function given by $ f(x) = \lg(x+1)-\frac{1}{2}\cdot\log_{3}x$. a) Solve the equation $ f(x) = 0$. b) Find the number of the subsets of the set \[ \{n | f(n^{2}-214n-1998) \geq 0,\ n \in\mathbb{Z}\}.\]