Find the number of solutions of the equation $log (5 - x) - log (x - 7) = 5$

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Solution

$log (5 - x) - log (x - 7) = 5$ is valid when $5 - x > 0, x - 7 > 0$
$\Rightarrow x < 5 and x > 7 \Rightarrow x \in {\emptyset}$
Therefore, number of solutions are zero.
Ans: 0

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