Answer
Please see the graph.
Work Step by Step
$f(x)=ln x +3$
$x=e$
$f(x)=ln {x+3}$
$f(e)=ln {e +3}$
$f(e) =ln e +3$
$f(e) =1+3$
$f(e)=4$
$x=e^2$
$f(x)=ln {x} +3$
$f(e^2)=ln {e^2} +3$
$f(e^2) =ln {e^2}+3$
$f(e^2) =2+3$
$f(e^2)=5$
$x=e^3$
$f(x)=ln {x+3}$
$f(e^3)=ln {e^3} +3$
$f(e^3) =3+3$
$f(e^3) =6$
$(e,4)$, $(e^2,5)$, and $(e^3,6)$ are on the curve.