Question 267986
I just provided help for a very similar problem. So please <A HREF="http://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.268070.html"> Click here</A> to view it. It will help you figure out how to find the base 4 logarithms and the asymptotic line.

P.S. x = -4 is a vertical line through -4 on the x-axis.
P.P.S. Most of the points you sent in the second message are not correct. You should be using:
{{{y = -log((x+4))/log((4))}}}
to find your coordinates.
When x =0
{{{y = -log((0+4))/log((4)) = -log((4))/log((4)) = -1}}}
When x = -1
{{{y = -log((-1+4))/log((4)) = -log((3))/log((4)) = -0.79}}}
When x = -3.975
{{{y = -log((-3.975+4))/log((4)) = -log((0.025))/log((4)) = 2.66}}}
With the correct points and an asymptote at x = -4 the graph should look like:
{{{graph(400, 400, -5, 5, -5, 5, -log(4, x+4))}}}