Originally Posted by

**x3bnm** I need help with a problem I found in a Discrete Mathematics book.

The problem is:

Prove that the $\displaystyle \lfloor{\log_{2} n}\rfloor + 1$ is $\displaystyle O(\log_{2} n)$ or $\displaystyle \lfloor{\log_{2} n}}\rfloor + 1$ is big-oh of $\displaystyle \log_{2} n$

So according to the definition of Big-O notation we have to show that:

$\displaystyle \lvert{\lfloor \log_{2} {n} \rfloor + 1} \rvert \leq M * \lvert{\log_{2} n}\rvert $

Now what property of logarithm proves that:

$\displaystyle \lvert{\lfloor{\log_{2}n}\rfloor + 1}\rvert \leq M * \lvert{\log_{2}n}\rvert $

From my knowledge I can't find a way to prove this. Can anyone kindly help me with this?