Let $f(x)=\ln{x}$ and $g(x)=\cfrac{1}{2}\ln{x-3}$. Which of the following transformations have been applied to $f(x)$ in order to obtain $g(x)$? Select ALL that apply.

A

Shifted left $3$ units

B

Shifted right $3$ units

C

Vertically compressed by a factor of $\cfrac{1}{2}$

D

Vertically compressed by a factor of $2$

E

Horizontally compressed by a factor of $\cfrac{1}{2}$