List the transformations that will change the graph of g(x)=lnx into the graph of the given function h(x)=log(x+3)-8

a) Horizontally shift the graph to the right by 3; then vertically shift downward by 8.
b) Horizontally shift the graph to the left by 8; then vertically shift downward by 3.
c) Horizontally shift the graph to the right by 3; then vertically shift upward by 8.
d) Horizontally shift the graph to the left by 3; then vertically shift downward by 8.
e) Horizontally shift the graph to the right by 8; then vertically shift downward by 3.

To determine the transformations that will change the graph of g(x) = lnx into the graph of h(x) = log(x+3)-8, we need to consider the effect of each term individually.

1) Horizontal shift:
The horizontal shift is determined by the term inside the logarithm function. In this case, the term is x+3, which means the graph will shift horizontally to the left by 3 units.

2) Vertical shift:
The vertical shift is determined by the constant term outside the logarithm function. In this case, the constant term is -8, which means the graph will shift vertically downward by 8 units.

Therefore, the correct answer is:
a) Horizontally shift the graph to the right by 3; then vertically shift downward by 8.