Quick math question

Barley
How does the following expand;

(q + N )*ln(q +N)

I'm Trying to arrive at sterling approximation for the multiplicity for einstein solid where q>>N. Any tips appreciated.

Thanks

stunner5000pt
factor out the bigger of the two

$$q(1 + \frac{N}{q} \ln q(1 + \frac{N}{q})$$

i gues you could 'expand it using the log expansion
$$ln (1+x) = x - \frac{1}{2} x^2 + \frac{1}{3} x^3 - ...$$

Barley
Thanks,

I'm going to have to see my prof. on this one. I'll let you know how it works out if you'd like.