1. **Problem:** Use logarithms to calculate $$\frac{\sqrt{6.019 \times 10^2} \times 10^{2.38}}{3.0 \times 5.8}$$. 2. **Formula and rules:** - Use logarithm properties: $$\log(ab) = \log a + \log b$$ and $$\log\left(\frac{a}{b}\right) = \log a - \log b$$. - Square root can be written as power 0.5: $$\sqrt{x} = x^{0.5}$$. 3. **Step-by-step solution:** - Calculate $$\sqrt{6.019 \times 10^2} = (6.019 \times 10^2)^{0.5} = 6.019^{0.5} \times (10^2)^{0.5} = \sqrt{6.019} \times 10^{1}$$. - Approximate $$\sqrt{6.019} \approx 2.454$$. - So, numerator becomes $$2.454 \times 10^{1} \times 10^{2.38} = 2.454 \times 10^{3.38}$$. - Denominator is $$3.0 \times 5.8 = 17.4$$. 4. **Divide numerator by denominator:** $$\frac{2.454 \times 10^{3.38}}{17.4} = \frac{2.454}{17.4} \times 10^{3.38}$$. 5. **Simplify fraction:** $$\frac{2.454}{17.4} \approx 0.141\quad \Rightarrow \quad 0.141 \times 10^{3.38}$$. 6. **Rewrite:** $$0.141 \times 10^{3.38} = 1.41 \times 10^{-1} \times 10^{3.38} = 1.41 \times 10^{3.38 - 1} = 1.41 \times 10^{2.38}$$. 7. **Final answer:** $$\boxed{1.41 \times 10^{2.38}}$$. --- **Note:** Only the first problem is solved as per instructions.