A) \[0\]
B) \[1\]
C) \[2\]
D) infinite
Correct Answer: A
Solution :
[a] \[{{\log }_{0.6}}\left( {{\log }_{6}}\frac{{{x}^{2}}+x}{x+4} \right)<0\] \[\Rightarrow \,\,\,{{\log }_{6}}\left( \frac{{{x}^{2}}+x}{x+4} \right)>1\] \[\Rightarrow \,\,\,\frac{{{x}^{2}}+x}{x+4}>6\Rightarrow \frac{{{x}^{2}}+x}{x+4}-6>0\] \[\Rightarrow \,\,\,\frac{{{x}^{2}}-5x-24}{x+4}>0\] \[\Rightarrow \,\,\,\frac{(x-8)\,(x+3)}{x+4}>0\] \[\Rightarrow \,\,\,x\in (-4,\,-3)\cup (8,\infty )\]
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