Question

$log_2(x^2-x)^2-2log_2(x+2)=2$

Answer 1

$log_2(x^2-x)^2-2log_2(x+2)=2\ begin{cases} log_2dfrac{(x^2-x)^2}{(x+2)^2}=2\ x+2>0 end{cases}\ begin{cases} dfrac{(x^2-x)^2}{(x+2)^2}=4\ x>-2 end{cases}\ begin{cases} (x^2-x)^2-4(x+2)^2=0\ x>-2 end{cases}\ begin{cases} left[begin{array}{l} x^2-x+2(x+2)=0\ x^2-x-2(x+2)=0 end{array}right.\ x>-2 end{cases}\ begin{cases} left[begin{array}{l} x^2+x+4=0\ x^2-3x-4=0 end{array}right.\ x>-2 end{cases}$

$begin{cases} left[begin{array}{l} x=4\ x=-1 end{array}right.\ x>-2 end{cases}\ x=4$