If 1 2 _ 0.1 x 2 then - Vidyadip

MCQ

If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then

A
The maximum value of $x$ is $1/\sqrt {10} $
B
$x$ lies between $1/100$ and $1/\sqrt {10} $
C
The minimum value of $x$ is $1/100$
✓
All of These

✓

Answer

Correct option: D.

All of These

d
(d) ${1 \over 2} \le {\log _{0.1}}x \le 2$

${1 \over 2} \le {\log _{0.1}}\,x \Rightarrow {\log _{0.1}}{(0.1)^{1/2}} \le {\log _{0.1}}x$

$ \Rightarrow $${(0.1)^{1/2}} \ge x$ $ \Rightarrow $$x \le {1 \over {\sqrt {10} }}$

${\log _{0.1}}x \le 2 \Rightarrow {\log _{0.1}}x \le {\log _{0.1}}{(0.1)^2}$

$x \ge {(0.1)^2} \Rightarrow x \ge {1 \over {100}}$, ${1 \over {100}} \le x \le {1 \over {\sqrt {10} }}$.

Hence, ${x_{{\rm{max}}}} = {1 \over {\sqrt {10} }},{x_{{\rm{min}}{\rm{.}}}} = {1 \over {100}}$.

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