Question

lg(x+2) + lg(x-2) = lg(5x+10)

Answer 1

$\lg(x+2) + lg(x-2) = lg(5x+10) \ D_f:x+2>0 wedge x-2>0 wedge 5x+10>0\ D_f:x>-2 wedge x>2 wedge x>-2\ D_f:x>2\ lg(x+2)(x-2)=lg(5x+10)\ lg(x^2-4)=lg(5x+10)\ x^2-4=5x+10\ x^2-5x-14=0\ x^2+2x-7x-14=0\ x(x+2)-7(x+2)=0\ (x-7)(x+2)=0\ x=7 vee x=-2\ -2not in D_f Rightarrow x=7$