Question

If $2^{|\ln x-2|}=\frac{4}{2^{|\ln x|}}$, then complete set of values of $x$ is

• A. $[1, e ]$
• B. $\left[1, e ^2\right]$
• C. $\left[ e ^2, \infty\right)$
• D. $(0,1] \cup\left[ e ^2, \infty\right)$

Answer 1

Answer: (B)

$ 2^{|\ln x-2|}=2^{2-|\ln x|} $
$\Rightarrow|\ln x-2|+|\ln x|=2$
Using property
$| a |+| b |=| a - b | \Rightarrow ab \leq 0 $
$\therefore \ln x (\ln x -2) \leq 0$
$\Rightarrow 0 \leq \ln x \leq 2 \Rightarrow 1 \leq x \leq e ^2$