Question

The integral value of $x$, that satisfies $1<{\log }_2(x-2)\le 2$, is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$

For $\log$ to be defined,
$x-2>0\Rightarrow x>2$

Now, $1<{\log }_2(x-2)\le 2$
$\Rightarrow 2^1<x-2\le 2^2$
$\Rightarrow x\in (4,6]$
$\Rightarrow x=5\text{or}x=6$