1. **State the problem:** We need to find the magnitude $R$ of an earthquake given the energy released $E = 880$ kwh using the formula: $$R = 0.67 \log(0.37E) + 1.46$$ 2. **Substitute the value of $E$ into the formula:** $$R = 0.67 \log(0.37 \times 880) + 1.46$$ 3. **Calculate the product inside the logarithm:** $$0.37 \times 880 = 325.6$$ So, $$R = 0.67 \log(325.6) + 1.46$$ 4. **Calculate the logarithm (base 10):** $$\log(325.6) \approx 2.512$$ 5. **Multiply by 0.67:** $$0.67 \times 2.512 = 1.683$$ 6. **Add 1.46:** $$R = 1.683 + 1.46 = 3.143$$ 7. **Round to the nearest hundredth:** $$R \approx 3.14$$ **Final answer:** The magnitude of the earthquake is approximately $3.14$.