1. The problem is to evaluate $\log \frac{1}{2}$.\n\n2. Recall the logarithm rule: $\log \frac{a}{b} = \log a - \log b$.\n\n3. Applying this rule, we get: $$\log \frac{1}{2} = \log 1 - \log 2.$$\n\n4. We know that $\log 1 = 0$ because any number to the power 0 is 1.\n\n5. Therefore, $$\log \frac{1}{2} = 0 - \log 2 = -\log 2.$$\n\n6. The final answer is $$\boxed{-\log 2}.$$