A) \[\left( \frac{1}{125},\infty \right)\]
B) \[\left( -\infty ,\frac{1}{125} \right)\]
C) \[\left( 0,\frac{1}{125} \right)\]
D) none of these
Correct Answer: C
Solution :
[C]| As \[\sin \,e\simeq sin2.71=\] positive value less than 1 |
| \[{{\log }_{\sin e}}{{\log }_{3}}{{\log }_{0.2}}x<0\] |
| \[\Rightarrow {{\log }_{3}}{{\log }_{0.2}}x>1\] |
| \[\Rightarrow {{\log }_{0.2}}x>3\] |
| \[\Rightarrow x<{{(0.2)}^{3}}\] \[\left\{ {{(0.2)}^{3}}=0.08=\frac{1}{125} \right\}\] |
| \[\therefore \] solution set is \[\left( 0,\frac{1}{125} \right)\] |
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