1. **State the problem:** Simplify the expression $4 \log 8 + 4 \log 32$. 2. **Recall the logarithm property:** $a \log b = \log b^a$ and $\log x + \log y = \log (xy)$. 3. **Apply the power rule:** $$4 \log 8 = \log 8^4$$ $$4 \log 32 = \log 32^4$$ 4. **Calculate powers:** $$8^4 = (2^3)^4 = 2^{12} = 4096$$ $$32^4 = (2^5)^4 = 2^{20} = 1048576$$ 5. **Rewrite the expression:** $$\log 4096 + \log 1048576$$ 6. **Use the product rule:** $$\log (4096 \times 1048576)$$ 7. **Multiply the numbers:** $$4096 \times 1048576 = 2^{12} \times 2^{20} = 2^{32}$$ 8. **Simplify the logarithm:** $$\log 2^{32} = 32 \log 2$$ 9. **If base is 10, approximate:** $$\log 2 \approx 0.3010$$ $$32 \times 0.3010 = 9.632$$ **Final answer:** $$4 \log 8 + 4 \log 32 = 32 \log 2 \approx 9.632$$