What transformation happens from In x to 3 In x? Also, I had thought that 3 In x and In x^3 are the same, but the graphics calculator shows otherwise.
ln (x^3) is indeed equal to 3ln x
perhaps your calculator is reading your input as
(ln x)^3 which of course is different
verification by Wolfram:
http://www.wolframalpha.com/input/?i=plot+y+%3D+log%28x%5E3%29+%2C+y+%3D+3log%28x%29
now change your input line from ln(x^3) to ln(x) for the first equation and see how it affects the graph.
Also ignore the part of the graph to the left of the y-axis, it is undefined for x ≤ 0