Value of x which satisfy following equation ${log}_{2} (x - 1) > 4$ .

x > 17

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x < 17

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x = 17

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none of these

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Solution

The correct option is A $x > 17$
For ${log}_{2} (x - 1) > 4$
Log is defined when $x - 1 > 0 \Rightarrow x > 1$ ...(1)
Now ${log}_{2} (x - 1) > 4 \Rightarrow x - 1 = 2^{4} \Rightarrow x > 17$ ...(2)
From (1) and (2), we get
$x > 17$

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