A) \[(-2,-1)\]
B) \[(-2,3)\]
C) \[(-\,1,3)\]
D) \[(3,\infty )\]
Correct Answer: B
Solution :
[b]We have, \[{{\log }_{3}}(x+2)(x+4)+{{\log }_{1/3}}(x+2)<\frac{1}{2}{{\log }_{\sqrt{3}}}7\]?(i) |
\[(x+2)(x+4)>0,(x+2)>0\] |
\[\therefore \]\[x>-\,2\] |
Now, Eq. (i) becomes \[{{\log }_{3}}(x+2)(x+4)-{{\log }_{3}}(x+2)<{{\log }_{3}}7\] |
\[\Rightarrow \]\[{{\log }_{3}}(x+4)<{{\log }_{3}}7\] |
\[\Rightarrow \]\[x+4<7\] |
\[\Rightarrow \]\[x<3\] |
\[\therefore \]\[x\in (-2,3)\] |
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