smc

From the properties of logarithms, we know that $({\log }_{a}x)({\log }_{x}b)={\log }_{a}b$, and ${\log }_{x}b=\frac{1}{{\log }_{b}x}$. Thus, to satisfy the given equation, we are looking for values of $x$ when ${\log }_{b}x=\frac{1}{{\log }_{b}x}$, or when ${\log }_{b}x=\pm 1$. This happens either when $x=b$ or $x=\frac{1}{b}$. Thus we have $2$ solutions, consistent with answer choice $\boxed{2}$.