1. **State the problem:** We need to calculate the value of $K$ given the formula $$K = \frac{2.303}{30} \log \frac{0.30}{0.10}$$ and verify the intermediate steps. 2. **Formula and explanation:** The formula uses the logarithm of a ratio, which is common in chemistry and physics for rate constants or equilibrium constants. The constant 2.303 converts natural logarithm to base-10 logarithm. 3. **Calculate the logarithm:** $$\log \frac{0.30}{0.10} = \log 3 = 0.48$$ 4. **Substitute the value:** $$K = \frac{2.303}{30} \times 0.48$$ 5. **Simplify the fraction:** $$K = \cancel{\frac{2.303}{30}} \times 0.48 = 0.037$$ 6. **Interpretation:** The value $K = 0.037$ atm$^{-1}$ is the final result, indicating the constant calculated from the given logarithmic expression. This step-by-step shows how to handle logarithms and constants in formulas clearly and accurately.