Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.4 Evaluation Logarithms and the Change-of-Base Theorem - 4.4 Exercises - Page 458: 65

(a) $ 3$ (b) $ 6$ (c) $ 8$

Following the definition of Richter scale ratings, we have: (a) $R= log(\frac{I}{I_0})= log(\frac{1000I_0}{I_0})=log(1000)=3$ (b) $R= log(\frac{I}{I_0})= log(\frac{1000000I_0}{I_0})=log(1000000)=6$ (c) $R= log(\frac{I}{I_0})= log(\frac{100000000I_0}{I_0})=log(100000000)=8$