• # question_answer If $\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+x} \right)\mathbf{-lo}{{\mathbf{g}}_{\mathbf{5}}}\left( \mathbf{x+l} \right)\mathbf{=2}$, then the value of x is: A)  5                                B)  10C)  25D)  32

(c): $lo{{g}_{5}}({{x}^{2}}+x)-lo{{g}_{5}}(x+1)=2$ $\Rightarrow lo{{g}_{5}}\left( \frac{{{x}^{2}}+x}{x+1} \right)=2$ $\Rightarrow lo{{g}_{5}}\left[ \frac{x(x+1)}{x+1} \right]=2$ $\Rightarrow {{\log }_{5}}x=2\Rightarrow x={{5}^{2}}=25$