A) \[(-2,-1)\]
B) \[(-2,3)\]
C) \[(-1,3)\]
D) \[(3,\infty )\]
Correct Answer: B
Solution :
| \[\left( x+2 \right)\left( x+4 \right)>0.x+2>0\Rightarrow x>-2.\] |
| Now (1) can be written as |
| \[{{\log }_{3}}\left( x+2 \right)\left( x+4 \right)-{{\log }_{3}}\left( x+2 \right)<\frac{\left( \log 7 \right)/2}{\left( \log 3 \right)/2}\]\[\Rightarrow \]\[{{\log }_{3}}\left( x+4 \right)<{{\log }_{3}}7\]\[\Rightarrow \]\[x+4<7\operatorname{or}\,x<3.\] |
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