Ln(4.47x) Further Developement

1) On this - I would like to show the upper triangle sided by [ 1 , 1.57 , 1.16 ] 2) I have added ln(4.47x) which is the counter part to the value .47 - while .4 corresponds to the Normal Curve. Notice the Distance number 1 from point(U) 3) Study the Line Delta and see how it has equal values to the Normal Curve - Leading me to believe that the probabilities can be all located in this region bringing doubt to my mind as to, iff- the formula is being interpreted correctly. Additionally- From [ 0 to 1 ] is unique to the Ln(x) and e^(x) function in it's orientation to them; From [ -1 to 0 has no such orientation making me wonder about it's deviation - (Crossing Axis for Solutions) and it's interpretation? ] 4) e^(-.69) plays an important roll in this Geometry - It has both and X - Component (not shown ) and it's Y - Component