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Conditions on the Parameters of Logarithm Function

The number of...

Question

The number of integral solutions of the inequation ${log}_{2} (x - 1 | \leq 1$ is

A

4

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B

3

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C

2

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D

5

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Solution

The correct option is A 4
$Given that {log}_{2} (x - 1 | \leq 1 For {log}_{2} (x - 1 | to be defined, x - 1 \neq 0 \Rightarrow x \neq 1 . . . [1] {log}_{2} (x - 1 | \leq 1 \Rightarrow 0 < (x - 1 | \leq 2^{1} = 2 \Rightarrow - 2 \leq x - 1 \leq 2 \Rightarrow - 1 \leq x \leq 3 . . . [2] From [1] and [2], we get x = - 1, 0, 2, 3 Therefore, the number of integral solutions is 4 .$

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