$\text{ If }{\log }_4\left(x^2-1\right)-{\log }_4(x+1)=1\text{ then }x\text{ is equal to ? }$

$$\begin{gathered} \text{ Given: }{\log }_4\left(x^2-1\right)-{\log }_4(x+1)=1 \\ \Rightarrow {\log }_4\left[\frac{\left(x^2-1\right)}{(x+1)}\right]=1\left(\because {\log }_a\frac{m}{n}={\log }_{a}m-{\log }_{a}n\right) \\ \Rightarrow {\log }_4\left[\frac{(\mathrm{x}-1)(\mathrm{x}+1)}{(\mathrm{x}+1)}\right]=1 \\ \Rightarrow {\log }_4(x-1)=1 \\ \Rightarrow (x-1)=4 \\ \therefore x=5 \end{gathered}$$