Answer
False,
$\ln x+\ln(2x)= \ln(2x^{2})$
or
$\ln 3+\ln x$=$\ln(3x)$
Work Step by Step
Applying The Product Rule:
$\log_{\mathrm{b}}(\mathrm{M}\mathrm{N})=\log_{\mathrm{b}}\mathrm{M}+\log_{\mathrm{b}}\mathrm{N}$,
to the LHS we should have
$\ln x+\ln(2x)=\ln(x\cdot 2x)=\ln(2x^{2}),$
which is differrent to the problem statement's RHS.
So, the problem statement is false.
To make it true, change the RHS to $\ln(2x^{2}),$
------------------
Alternatively, we could have started from the RHS,
applying the Product Rule:
$\ln(3\cdot x)=\ln 3+\ln x,$
so the statement becomes true if you change the LHS to $\ln 3+\ln x$.
