Find the value of $x$ which satisfies the equation : $1 < {log}_{2} (x - 2) \leq 2$

4 < x \leq 6

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5 \leq x < 6

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6 < x < 8

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none of these

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Solution

The correct option is A $4 < x \leq 6$
Domain is $(x - 2) > 0 \Rightarrow x ϵ (2, \infty)$
$1 < {log}_{2} (x - 2) \leq 2$
$\Rightarrow 2^{1} < x - 2 \leq 2^{2}$
$\Rightarrow 4 < x \leq 6$

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