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Help with Schrodinger's Statistical Thermodynamics Text

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I was just wanting to see the steps in between for the two highlighted equations in the attached file from Schrodinger's Statistical Thermodynamics text. I just cannot seem to come up with the same 2nd equation in my calculations. Thank you very much! (the 'log' in the text is actually 'ln' or log base e)

** Please see the attached file for the complete problem description **

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