Finding a relationship between functions

[impendingChaos]

I posted on this tangent a little while ago but I've moved forward and was looking for some input.
I have two exponential equations each is described by a different variable (n and v respectively):

y=1.44E-24*exp(46.22n)+2.006E-8
y=2.88*exp(-2.4v)-3.009E-5

Since the end constants are so small I am considering them negligible so:

y=1.44E-24*exp(46.22n)
y=2.88*exp(-2.4v)

What I am trying to find is a relationship between variables n and v.

Currently I've tried taking the natural log of both sides to get:

ln(y)=ln(1.44E-24)+ln(exp(46.22n))
ln(y)=-54.897+56.22n
and
ln(y)=ln(2.88)+ln(exp(-2.4v))
ln(y)=1.058-2.4v

So in essence I now have two linear equations. Are there any suggestions to finding a numerical relationship between n and v. Is there value in finding the intersection of these two linear equations?

Thanks
C.N.

 

[matt grime]

If you don't mind me saying so, there is something odd in you asserting that things of the order 10^-5 are negligible, but that 10^-24 isn't.

y=something
y=something else

therefore something equals something else. That is a relation ship. It just isn't of the (unjustifiable preferred?) v=function of n.