1. **Problem statement:** Express the sum or difference of logarithms as a single logarithm. 2. **Formula and rules:** - The logarithm of a product: $\log_b(x) + \log_b(y) = \log_b(xy)$ - The logarithm of a quotient: $\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)$ - These rules apply only if the logarithms have the same base $b$. 3. **Example:** Suppose you have $\log_b(A) + \log_b(B) - \log_b(C)$. 4. **Step-by-step simplification:** - Combine the sum first: $\log_b(A) + \log_b(B) = \log_b(AB)$ - Then subtract: $\log_b(AB) - \log_b(C) = \log_b\left(\frac{AB}{C}\right)$ 5. **Explanation:** By using the product and quotient rules of logarithms, multiple logarithmic terms can be combined into a single logarithm representing the product or quotient inside the log. 6. **Final answer:** $$\log_b(A) + \log_b(B) - \log_b(C) = \log_b\left(\frac{AB}{C}\right)$$ This is the single logarithm expression equivalent to the original sum and difference of logarithms.