1. **State the problem:** Write the expression $6 \log_8 x + 3 \log_8 z$ as a single logarithm. 2. **Recall the logarithm power rule:** For any positive $a$, $b$, and base $c > 0$, $c \neq 1$, we have $k \log_c a = \log_c a^k$. 3. **Apply the power rule to each term:** $$6 \log_8 x = \log_8 x^6$$ $$3 \log_8 z = \log_8 z^3$$ 4. **Use the logarithm addition rule:** $\log_c A + \log_c B = \log_c (AB)$. 5. **Combine the two logarithms:** $$\log_8 x^6 + \log_8 z^3 = \log_8 (x^6 z^3)$$ 6. **Final answer:** $$6 \log_8 x + 3 \log_8 z = \log_8 (x^6 z^3)$$ This expresses the original sum as a single logarithm.