Question
Solve the following:$\log (3 - x) - \log (x - 3) = 1$
✓
Answer
$\log (3-x)-\log (x-3)=1 $
$ \Rightarrow \log \left(\frac{3-x}{x-3}\right) $
$ =1 $
$=\log 10$
$ \Rightarrow\left(\frac{3-x}{x-3}\right)=10 $
$\Rightarrow 3-x=10(x-3) $
$ \Rightarrow 3-x=10 x-30$
$ \Rightarrow 11 x=33$
$ \Rightarrow x=3 .$
$ \Rightarrow \log \left(\frac{3-x}{x-3}\right) $
$ =1 $
$=\log 10$
$ \Rightarrow\left(\frac{3-x}{x-3}\right)=10 $
$\Rightarrow 3-x=10(x-3) $
$ \Rightarrow 3-x=10 x-30$
$ \Rightarrow 11 x=33$
$ \Rightarrow x=3 .$
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