Grunberg-Nissan Equation Proof

[syki]

Homework Statement

Prove:

ln(η) = Σ[xi*ln(ηi)]

2. The attempt at a solution

I tried using the relationship:

Σ(xi)=1

and the rules for adding logarithms, but I seem to be totally failing at this. I'm not asking to have it worked out, but any hints on which direction I should go?

 

[Borek]

From what I understand this is a semiempirical equation, so there is nothing to prove - you can at best test its applicability experimentally.

 

[syki]

I was told to, specifically, prove the relationship:

ln(η) ≈ x1*ln(η1) + x2*ln(η2)

is true mathematically. I'm not really sure how to go about that.