1. **Problem Statement:** Given that $\log a = 0.30$ and $\log b = 0.45$, find the value of $\log \frac{b^2}{a}$. 2. **Formula and Rules:** We use the logarithm properties: - $\log \frac{M}{N} = \log M - \log N$ - $\log M^k = k \log M$ 3. **Apply the formula:** $$\log \frac{b^2}{a} = \log b^2 - \log a$$ 4. **Use the power rule:** $$\log b^2 = 2 \log b$$ 5. **Substitute the given values:** $$= 2 \times 0.45 - 0.30$$ 6. **Calculate:** $$= 0.90 - 0.30 = 0.60$$ **Final answer:** $$\boxed{0.60}$$