Answer
False
Work Step by Step
$\ln (x+1)=\ln x+\ln 1$
Since, $\ln m+\ln n=\ln (\dfrac{m}{n})$
Thus, $\ln (x+1)=\ln (\dfrac{x}{1})$
Let us write the correct statement such as:
or, $\ln (x+1)=\ln x$
which is not true.
Hence, the given statement is false.