Answer
$x=0;x=3$
Work Step by Step
$\log _{2}\left( x-2\right) +\log _{2}\left( x-1\right) =1\Rightarrow \log _{2}\left[ \left( x-1\right) \left( x-2\right) \right] =1$
$\Rightarrow x^{2}-3x+2=2^{1}\Rightarrow x^{2}=3x\Rightarrow x=0;x=3$
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