Big O Proof for Logarithmic Function I am an undergraduate student in Computer Engineering and going through one of the textbook examples, I am asked to prove that 

$T(n)$ is $O(\log{}n)$

Where $T(n)= 5\log_{2} 2n +7$.
I understand that this means that I must prove that $5\log_{2} 2n +7 \leq\lambda log(n)$

For some in n in a neighborhood of infinity. How exactly would I proceed with this?
$$5\log_2(2n)+7=5\log_2 n+5\log_2 2+7=5\log_2 n +12$$
Since for example $12\le 12\log_2 n$ for $n\ge 2$, it follows that
$$5\log_2 n +12\le 5\log_2 n +12\log_2 n=17\log_2 n $$
for $n\ge 2$. This yields $O(\log n) $.