Question

2log2(x-1)-log2(2x-4)>0

Answer 1

$2log_2(x-1)-log_2(2x-4)>0\\\left \{ {{x-1> 0 } \atop {2x-4> 0}} \right. =>x>2\\log_2(x-1)^2>log_2(2x-4)\\log_2(\frac{x^2-2x+1}{2(x-2)} )>0\\\frac{x^2-2x+1}{2(x-2)}>1\\\frac{x^2-4x+5}{2(x-2)}>0\\\frac{1}{x-2}>0\\x>2$

x∈(2;+∞)