e raised to the power of y-length subtract h-length

OB = 1
OA = L
BA = X
AB is perpendicular to OB
OBC and AOB are similiar triangles
angle OBC and AOB are equal

y-length of AB relative to O:
y-length = ln(L + X)
h-length of AB relative to O:
h-length = ln(L)

If h-length is subtracted from y-length, and the difference is used as an exponent to the base e, that amount equals 1 + OC.

e^{ylength - hlength} = 1 + OC

in the diagram:
AB = .57735
OA = 1.1547
OC = .5

e^{.549306 - .143841}
= e^.405464
= 1.5
= 1 + .5