If $j − 1 < \log k < j$. Why is $j = O(\log k)$? If $j \in Z^+$ and $k \in R^+$ and $j − 1 &lt; \log k &lt; j$. Why is $j = O(\log k)$? (All log's are in base 2)
I know I have to find constants where $j &lt;= c \cdot \log k$ but I need some help with it.
You solved your own question. Quite literally the bounds you gave (with $c=1$ or $c=2$) should suffice