Answer:
[tex]g(x)=\log (x+1)+4[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: [tex]f(x)=\log x[/tex]
From inspection of the graph, the parent function has been translated 1 unit left and 4 units up.
Function translated 1 unit left: [tex]f(x+1)=\log (x+1)[/tex]
Function translated 4 units up: [tex]f(x+1)+4=\log (x+1)+4[/tex]
Therefore:
[tex]g(x)=\log (x+1)+4[/tex]
