Why Bases Don't Matter in Big-O (Constant factor)

In Big-O notation, we write $O(\log n)$ without specifying the base. Why? Because changing the base only multiplies by a constant.

From the change of base formula: $\log_2(n) = \frac{\log_{10}(n)}{\log_{10}(2)} \approx 3.32 \cdot \log_{10}(n)$. The factor $3.32$ is constant, and Big-O ignores constants.

So when you see $O(\log n)$ in algorithm analysis, the base is usually $2$ (because of binary splits), but it doesn't matter for asymptotic analysis.