Is the following true? log2(2n) ∈ O(log2(n))?
We have:
$$\log_2(2n) = \log_2(2) + \log_2(n) = 1 + \log_2(n) &lt; 2 \times \log_2(n)$$

You can take $c = 2$ and as $\log_2(2n) &lt; c \times \log_2(n)$ for $n &gt; 2$, we can say $\log_2(2n) \in O(\log_2(n))$.