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 :
| As sine\[\simeq \] sin 2.71 = positive value less than 1 |
| \[{{\log }_{\text{sine}}}{{\log }_{3}}{{\log }_{0.2}}x<0\] |
| \[\Rightarrow \]\[{{\log }_{3}}{{\log }_{0.2}}x<1\] \[\Rightarrow \]\[{{\log }_{0.2}}x>3\] \[\Rightarrow \]\[x<{{(0.2)}^{3}}\] |
| \[\{{{(0.2)}^{3}}=.008=\frac{1}{125}\}\] |
| \[\therefore \] solution set is \[\left( 0,\,\,\frac{1}{125} \right)\] |
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