I thought they did, but recently I tried to express $3^n$ as $k \times 2^n + o(2^n)$ for some constant $k$ but wasn't able to. All I found was $3^n = (\frac{3}{2})^n 2^n$. What am I misunderstanding here?
I suppose my question applies to $log_c(n) = O(log_2(n))$ as well.