To determine the vertical asymptote of the function [tex]\( f(x) = 3 \log (x + 3) \)[/tex], we need to consider where the argument of the logarithm is equal to zero since the logarithmic function becomes undefined at that point.
The argument of the logarithm in this function is [tex]\( x + 3 \)[/tex].
To find where this argument equals zero, we solve the equation:
[tex]\[ x + 3 = 0 \][/tex]
Subtract 3 from both sides:
[tex]\[ x = -3 \][/tex]
Therefore, the vertical asymptote of the function [tex]\( f(x) = 3 \log (x + 3) \)[/tex] is
[tex]\[ x = -3 \][/tex]
Thus, the correct answer is
[tex]\[ \boxed{-3} \][/tex]
