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\\ -2\not \in D_f \Rightarrow x=7" alt="\\\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\\ -2\not \in D_f \Rightarrow x=7" align="absmiddle" class="latex-formula">