Lg(x-1)+Lg(x+1)=0
ОДЗ: 
0\\x+1>0 \end{cases}" alt="\begin{cases} x-1>0\\x+1>0 \end{cases}" align="absmiddle" class="latex-formula">
1\\x>-1 \end{cases}" alt="\begin{cases} x>1\\x>-1 \end{cases}" align="absmiddle" class="latex-formula">
⇒ x>1
lg((x-1)(x+1))=0
lg(x²-1)=0
x²-1=1
x²=2
x=√2