The number of integral value(s) of $x$ that are not in domain of $f (x) = log (\frac{1}{| 2 x - 3 |}) + \frac{1}{log (| 2 x - 3 |)}$ is

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Solution

Given : $f (x) = log (\frac{1}{| 2 x - 3 |}) + \frac{1}{log (| 2 x - 3 |)}$
For domain,
$| 2 x - 3 | \neq 0 \Rightarrow x \neq \frac{3}{2} | 2 x - 3 | \neq 1 \Rightarrow x \neq 1, 2$

$∴$ The number of integral values of $x$ is $2.$

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