Quotient Rule (Division becomes subtraction)

When you divide two numbers inside a logarithm, you can split it into a difference: $\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$.

For example, $\log_2\left(\frac{32}{4}\right) = \log_2(32) - \log_2(4) = 5 - 2 = 3$. And indeed, $\log_2(8) = 3$.

This turns division into subtraction. Combined with the product rule, you can break down complex expressions into simpler pieces.