Answer
${\text{False}}$
Work Step by Step
$$\eqalign{
& {\text{Let }}f\left( x \right) = \log x{\text{ and }}g\left( x \right) = \ln x \cr
& {\text{Differentiating}} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left[ {\log x} \right] \cr
& f'\left( x \right) = \frac{1}{{x\left( {\ln 10} \right)}}\frac{d}{{dx}}\left[ x \right] \cr
& f'\left( x \right) = \frac{1}{{x\left( {\ln 10} \right)}} \cr
& and \cr
& g'\left( x \right) = \frac{d}{{dx}}\left[ {\ln x} \right] \cr
& g'\left( x \right) = \frac{1}{x} \cr
& \frac{1}{{x\left( {\ln 10} \right)}} \ne \frac{1}{x} \cr
& {\text{The derivatives are not equal, the statement is False}} \cr} $$
