1. **State the problem:** Rewrite $\log_7 \left(x^5 (x - 4)\right)$ without exponents. 2. **Recall logarithm rules:** - $\log_b (MN) = \log_b M + \log_b N$ (log of a product is sum of logs) - $\log_b (M^k) = k \log_b M$ (log of a power is exponent times log) 3. **Apply product rule:** $$\log_7 \left(x^5 (x - 4)\right) = \log_7 x^5 + \log_7 (x - 4)$$ 4. **Apply power rule:** $$\log_7 x^5 = 5 \log_7 x$$ 5. **Combine results:** $$\log_7 \left(x^5 (x - 4)\right) = 5 \log_7 x + \log_7 (x - 4)$$ 6. **Rewrite without exponents:** The expression is now a sum of logarithms with no exponents inside the logs. **Final answer:** $$5 \log_7 x + \log_7 (x - 4)$$