[tex]3-x\not =0 \wedge \dfrac{x-2}{3-x}>0 \wedge\log_{1/7}\left(\dfrac{x-2}{3-x}\right)-1>0\\\\\\3-x\not=0\\x\not=3\\\\\\\dfrac{x-2}{3-x}>0\\(x-2)(3-x)>0\\-(x-2)(x-3)>0\\x\in(2,3)\\\\\\\log_{1/7}\left(\dfrac{x-2}{3-x}\right)-1>0\\\\\log_{1/7}\left(\dfrac{x-2}{3-x}\right)>1\\\log_{1/7}\left(\dfrac{x-2}{3-x}\right)>\log_{1/7}\dfrac{1}{7}\\\\\dfrac{x-2}{3-x}<\dfrac{1}{7}\\\\7(x-2)<3-x\\7x-14<3-x\\8x<17\\x<\dfrac{17}{8}=2\dfrac{1}{8}[/tex]
[tex]x\not =3 \wedge x\in(2,3) \wedge x<2\dfrac{1}{8}\\\\\boxed{\boxed{x\in\left(2,2\dfrac{1}{8}\right)}}[/tex]
