Answer
The statement $\ln \left( ab \right)=\ln a-\ln b$ is false.
Work Step by Step
$\ln \left( ab \right)=\ln a-\ln b$
The properties of common logarithms are applicable for natural logarithms as well.
The product rule for logarithms says that, for any positive numbers M, N and a $\left( a\ne 1 \right)$, ${{\log }_{a}}\left( MN \right)={{\log }_{a}}M+{{\log }_{a}}N$.
Therefore, $\ln \left( ab \right)=\ln a+\ln b$.
In the statement, it is given as $\ln \left( ab \right)=\ln a-\ln b$.
