[tex]\displaystyle\bf\\lg(x-1)=-1\\\\x-1=10^{-1}\\\\x-1=\frac{1}{10}~~\Big|\cdot10\\\\10(x-1)=1\\\\10x-10=1\\\\10x=1+10\\\\10x=11\\\\\boxed{\bf x=\frac{11}{10}}[/tex]
