1. If $a>1, b>1$ and $\lg (a+b)=\lg a+\lg b$, then the value of $\lg (a-1)+\lg (b-1)$
(A) equals $\lg 2$
(B) equals 1
(C) equals 0
(D) is not a constant independent of $a, b$
(C)
I. Multiple Choice Question
1.【Analysis and Solution】 $\because \lg (a+b)=\lg a+\lg b$, $\therefore a+b=a b$, i.e., $(a-1)(b-1)=1$. Therefore, $\lg (a-1)+\lg (b-1)=0$.