• # question_answer Solution set of inequality ${{\log }_{\sin \,\,e}}{{\log }_{3}}{{\log }_{0.2}}x<0$ is (where e is Napier's constant) 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

 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 $\left( 0,\,\,\frac{1}{125} \right)$