Common Logarithm Mistakes (Pitfalls to avoid)

$1.$ Confusing $\log(n)$ with $\log(\log(n))$. The latter is much smaller (double logarithm) and appears in advanced data structures like van Emde Boas trees.

$2.$ Forgetting that $\log(ab) = \log(a) + \log(b)$, not $\log(a) \times \log(b)$. Logarithms turn multiplication into addition.

$3.$ Assuming $O(\log n)$ means the algorithm divides the input. Not always. Sometimes the input size is fixed but the value range is halved (like binary search on values).