Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
Consider the parent function
[tex]y=\log _5x[/tex]
This function is defined for all [tex]x>0,[/tex] so vertical line with equation [tex]x=0[/tex] is its vertical asymptote.
Function [tex]F(x)=2\log_5(x+1)-3[/tex] can be obtained from parent function by translation 1 unit to the left and 3 units down. This translation transletes the vertical asymptote [tex]x=0[/tex] of the parent function into the vertical asymptote [tex]x=-1[/tex] of function [tex]F(x).[/tex]
