Question

Solve :
$lo{g}_{x}0.5>2$

• A. $(\sqrt{1/2},1)$
• B. $(-\infty ,1)$
• C. $(-1,0)$
• D. $(-1,1)$

Answer 1

The correct option is A $(\sqrt{1/2},1)$

$\begin{array}{c}{\log }_{x}0.5>2\\ -{\log }_{x}2>2\\ {\log }_{x}2<-2\\ x\in \left(\frac{1}{\sqrt{2}},1\right)\end{array}$

Hence,

Option$\begin{array}{c}{\log }_{x}0.5>2\\ -{\log }_{x}2>2\\ {\log }_{x}2<-2\\ x\in \left(\sqrt{\frac{1}{2}},1\right)\end{array}$

Hence,

Option $A$ is correct answer.