Question 982516
Since the log function increases as x increase, you can just solve for the argument inequality.
{{{4(2-x)>2x}}}
{{{8-4x>2x}}}
{{{8>6x}}}
{{{x<8/6}}}
{{{x<4/3}}}
An additional requirement is that both arguments remain positive since log function can only have positive arguments.
{{{4(2-x)>0}}}
{{{2-x>0}}}
{{{x<2}}}
and
{{{2x>0}}}
{{{x>0}}}
So all three of these requirements must be met simultaneously leading to,
{{{0<x<4/3}}}