Question 440076
{{{ln(4-x) + ln2 = lnx^2}}}
<==> {{{ln(2(4-x)) = lnx^2}}}
<==> {{{2(4-x) = x^2}}}
<==> {{{x^2 + 2x -8=0}}}
<==> (x + 4)(x-2) = 0 ==> x = -4, 2.

We cannot accept the solution x = -4 since it doesn't satisfy the original equation.  X=2 satisfies the original equation, so is the final answer.