> [!NOTE] Lemma > Let $f:\mathbb{N}\to \mathbb{R}$ be a [[Real sequences|real sequence]]. For all $a,b>0,$ $f(n)$ is [[Big O Relation on Real Sequences|big O]] of $\log_{a}n$ iff $f(n)=\mathcal{O}(\log_{b}n).$ **Proof**: ...