First sketch the parent graph $y=\log(x)$.
Two points on this curve are $(1,0)\ \text{and}\ (10,1)$.
There is a vertical asymptote of $x=0$.

Use the Order of Operations when transforming functions.
Begin by shifting the curve left $4$ units.
The two points are now $(−3,0)\ \text{and}\ (7,1)$. The vertical asymptote is $x = −4$.

Next, apply the vertical stretch factor of $3$.
This means $(−3,0)$ remains in place, but $(7,1)$ becomes $(7,3)$.
The vertical asymptote is still $x=−4$.

Finally, shift the curve down $1$ unit.