1. **State the problem:** Find the value of $\log \frac{1}{4}$. 2. **Recall the logarithm rule:** $\log \frac{a}{b} = \log a - \log b$. 3. **Apply the rule:** $\log \frac{1}{4} = \log 1 - \log 4$. 4. **Evaluate known logs:** $\log 1 = 0$ because any number to the power 0 is 1. 5. **Simplify:** $\log \frac{1}{4} = 0 - \log 4 = -\log 4$. 6. **Express $\log 4$:** Since $4 = 2^2$, $\log 4 = \log 2^2 = 2 \log 2$. 7. **Final answer:** $\log \frac{1}{4} = -2 \log 2$.