Don't understand how log rules are applied in formula

Question

On page 148 of Computational Complexity by Papadimitriou, it states:

$nc_1^{f(n)} = c_1^{\log(n) + f(n)}$

I understand that I can expand the right part of the formula to $c_1^{\log(n) + f(n)} = c_1^{\log(n)}c_1^{f(n)}$, but then why and how does $c_1^{\log(n)} = n$?