[tex]D:5x-2>0 \wedge x>0 \wedge x-1>0\\
D:5x>2 \wedge x>0 \wedge x>1\\
D: x>\frac{2}{5} \wedge x>1\\
D:x>1\\
\log_2(5x-2)-\log_2x-\log_2(x-1)=2\\
\log_2\frac{5x-2}{x(x-1)}=\log_24\\
\frac{5x-2}{x(x-1)}=4\\
4x(x-1)=5x-2\\
4x^2-4x=5x-2\\
4x^2-9x+2=0\\
4x^2-x-8x+2=0\\
x(4x-1)-2(4x-1)=0\\
(x-2)(4x-1)=0\\
x=2 \vee x=\frac{1}{4}\\
\frac{1}{4}\not \in D \Rightarrow \boxed{x=2}
[/tex]
