1. **Problem:** Condense the expression $6 \log 2 + 2 \log 12 - 3 \log 4$ into a single logarithm and find its value. 2. **Formula and rules:** - Use the logarithm power rule: $a \log b = \log b^a$ - Use the logarithm product rule: $\log a + \log b = \log (ab)$ - Use the logarithm quotient rule: $\log a - \log b = \log \left(\frac{a}{b}\right)$ 3. **Apply power rule:** $$6 \log 2 + 2 \log 12 - 3 \log 4 = \log 2^6 + \log 12^2 - \log 4^3$$ 4. **Simplify powers:** $$\log 64 + \log 144 - \log 64$$ 5. **Apply product and quotient rules:** $$\log \left(64 \times 144 \right) - \log 64 = \log \left(\frac{64 \times 144}{64}\right)$$ 6. **Cancel common factor:** $$\log \left(\cancel{64} \times 144 / \cancel{64}\right) = \log 144$$ 7. **Evaluate:** $$\log 144$$ Assuming base 10, approximate value: $$\log 144 \approx 2.1584$$ **Final answer:** $\log 144 \approx 2.16$