Answer
${\text{ True}}$
Work Step by Step
$$\eqalign{
& {\text{Let }}f\left( x \right) = \ln \left( {kx} \right){\text{ and }}g\left( x \right) = \ln x \cr
& {\text{Differentiating}} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left[ {\ln \left( {kx} \right)} \right] \cr
& f'\left( x \right) = \frac{k}{{kx}} \cr
& f'\left( x \right) = \frac{1}{x} \cr
& and \cr
& g'\left( x \right) = \frac{d}{{dx}}\left[ {\ln x} \right] \cr
& g'\left( x \right) = \frac{1}{x} \cr
& {\text{The derivatives are equal, the statement is True}} \cr} $$
