1. **State the problem:** Write the expression $3 \log 2 - \frac{1}{2} \log 16$ as a single logarithm. 2. **Recall logarithm rules:** - $a \log b = \log b^a$ (power rule) - $\log a - \log b = \log \frac{a}{b}$ (quotient rule) 3. **Apply the power rule:** $$3 \log 2 = \log 2^3 = \log 8$$ $$\frac{1}{2} \log 16 = \log 16^{\frac{1}{2}} = \log \sqrt{16} = \log 4$$ 4. **Rewrite the expression:** $$3 \log 2 - \frac{1}{2} \log 16 = \log 8 - \log 4$$ 5. **Apply the quotient rule:** $$\log 8 - \log 4 = \log \frac{8}{4} = \log 2$$ **Final answer:** $\log 2$ which corresponds to option b.