Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
The function [tex]y=\log x[/tex] is defined for all [tex]x>0[/tex] and has the vertical asymptote [tex]x=0.[/tex]
The function [tex]y=\log (x+3)-8[/tex] is translated 3 units to the left and 8 units down function [tex]y=\log x[/tex].
This means that the vertical asymptote of the function [tex]y=\log (x+3)-8[/tex] is translated 3 units to the left vertical asymptote of the function [tex]y=\log x.[/tex]
The equation of this asymptote is [tex]x=-3.[/tex]
