If _5 ( x^2 + x ) - _5 ( x + 1 ) = 2, then the value of x is -

Answer: Option C

$$\begin{array}{rl}& {\log }_5\left(x^2+x\right)-{\log }_5\left(x+1\right)=2\\ & \Rightarrow {\log }_5\left(\frac{x^2+x}{x+1}\right)=2\\ & \Rightarrow {\log }_5\left[\frac{x\left(x+1\right)}{x+1}\right]=2\\ & \Rightarrow {\log }_{5}x=2\\ & \Rightarrow x=5^2\\ & =25\end{array}$$