find the slope and the constant of an equation of a curve

hi there friends. the issue is i finding the slope and the constant.

http://cse.yeditepe.edu.tr/~byilmaz/fall2010/cse112/homeworks/cse112HW5.pdf

in this homework i can find slope and the constant of a straigth line but the formula for finding slope and constant doesn't work for a curve. and i don't understand why she takes the logarithm of curve's equation.
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