How do you solve $log (5+x) - log (x-2) = log 2$ ?

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Answer 1 · 2018-07-17T15:03:12

$x=9$

Given equation:

$log(5+x)-\log(x-2)=\log2\quad (\forall \ \ x>2)$

$\log({5+x}/{x-2})=\log 2$

Comparing the numbers on both the sides, we get

${5+x}/{x-2}=2$

$5+x=2x-4$

$x=5+4$

$x=9$

How do you solve log (5+x) - log (x-2) = log 2log (5+x) - log (x-2) = log 2?