A) (1, 2)
B) \[(0,\text{ }1)\]
C) \[(1,\infty )\]
D) \[(2,\infty )\]
E) \[(0.09,0.3)\]
Correct Answer: D
Solution :
\[{{\log }_{0.3}}(x-1)<{{\log }_{0.09}}(x-1)\] \[\Rightarrow \] \[{{\log }_{0.3}}(x-1)<{{\log }_{{{(0.3)}^{2}}}}(x-1)\] \[\Rightarrow \] \[{{\log }_{0.3}}(x-1)<\frac{1}{2}{{\log }_{0.3}}(x-1)\] \[\Rightarrow \] \[{{\log }_{0.3}}(x-1)<0\] \[\Rightarrow \] \[(x-1)>1\Rightarrow x>2\]and \[x>1\] \[\therefore \] \[x\in (2,\infty )\]
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