Thermodynamics(math) derivation step

  • Thread starter iScience
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hi, i just need help with a step in a derivation in my thermodynamics book (indicated by the red arrow)



http://i.imgur.com/C8k3xzT.jpg

firstly, what's the point of a -(q+N) term if they're just going to cancel it out with a +q and +N?

basically i want to know how the terms inside the 'ln' can come out in front.
 

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