Power Rule (Exponent comes out front)

When you take the logarithm of a power, the exponent moves out front as a multiplier: $\log_b(x^k) = k \cdot \log_b(x)$.

For example, $\log_2(8^2) = 2 \cdot \log_2(8) = 2 \cdot 3 = 6$. And indeed, $\log_2(64) = 6$.

This is the most powerful property for complexity analysis. When you have $\log(n^2)$, you can simplify it to $2 \log n$, which is still $O(\log n)$ because the constant $2$ drops in Big-O notation.