A) 5
B) 10
C) 25
D) 32
Correct Answer: C
Solution :
(c): \[lo{{g}_{5}}({{x}^{2}}+x)-lo{{g}_{5}}\left( x+1 \right)=2\] \[\Rightarrow \,\,\,\,{{\log }_{5}}\left( \frac{{{x}^{2}}+x}{x+1} \right)=2\] \[\Rightarrow \,\,\,\,{{\log }_{5}}\left( \frac{x(x+1)}{x+1} \right)=2\] \[\Leftrightarrow lo{{g}_{5}}x=2\,\Leftrightarrow x={{5}^{2}}=25\]
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