Answer
{$2\sqrt 2$}
Work Step by Step
Step 1: $\log_{2} x+\log_{2} 2x-3=1$
Step 2: $\log_{2} (x\times2x)=1+3$
Step 3: $\log_{2} (2x^{2})=4$
Step 4: $2x^{2}=2^{4}$
Step 5: $2x^{2}=16$
Step 6: $x^{2}=8$
Step 7: $x=\sqrt 8=2\sqrt 2$
Therefore, the solution set is {$2\sqrt 2$}.
