1. **State the problem:** Given that $\log 40 = a$, express $\log 4$ in terms of $a$. 2. **Recall the logarithm properties:** - $\log xy = \log x + \log y$ - $\log \frac{x}{y} = \log x - \log y$ 3. **Express 40 in terms of 4:** $$40 = 4 \times 10$$ 4. **Use the product rule for logarithms:** $$\log 40 = \log (4 \times 10) = \log 4 + \log 10$$ 5. **Substitute the given value:** $$a = \log 4 + \log 10$$ 6. **Recall that $\log 10 = 1$ (common logarithm base 10):** $$a = \log 4 + 1$$ 7. **Solve for $\log 4$:** $$\log 4 = a - 1$$ **Final answer:** $$\boxed{\log 4 = a - 1}$$