The number of solutions of the equation
$| ln | x | | - | | x | - 1 | = 0$ is

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Solution

For
$x > 1 \Rightarrow x - 1 > ln x$
Therefore, the graph $y = x - 1$ does not intersect $y = ln x$ when $x > 1$
Similarly, for
$x < - 1 \Rightarrow - x - 1 > ln (- x)$
$\Rightarrow$ The graph $y = - x - 1$ does not intersect $y = ln (- x)$ when $x < - 1$

$\Rightarrow$ Only 2 solutions i.e. $(- 1, 0) & (1, 0)$

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