1. **State the problem:** Expand the logarithm $\log_v u^5 w$ as a sum or difference of logarithms with base $v$. 2. **Recall the logarithm properties:** - Product rule: $\log_v (AB) = \log_v A + \log_v B$ - Power rule: $\log_v (A^k) = k \log_v A$ 3. **Apply the product rule:** $$\log_v u^5 w = \log_v u^5 + \log_v w$$ 4. **Apply the power rule to the first term:** $$\log_v u^5 = 5 \log_v u$$ 5. **Combine the results:** $$\log_v u^5 w = 5 \log_v u + \log_v w$$ This is the expanded form of the logarithm as a sum of multiples of base-$v$ logarithms.