Product Rule (Multiplication becomes addition)

When you multiply two numbers inside a logarithm, you can split it into a sum: $\log_b(xy) = \log_b(x) + \log_b(y)$.

For example, $\log_2(8 \times 4) = \log_2(8) + \log_2(4) = 3 + 2 = 5$. And indeed, $\log_2(32) = 5$.

This property turns multiplication into addition, which makes calculations easier. You'll use this when analyzing nested loops or recursive algorithms that split problems into multiple parts.