Chapter 4, Exponential and Logarithmic Functions - Section 4.7 - Logarithmic Scales - 4.7 Exercises - Page 422: 10

a) $5.9$ b) $63$ cm

We know that $M=\log\frac{I}{S}$ and thus $10^M=\frac{I}{S}$ a) Hence, here if $I=72.1$, we have: $M=\log\frac{72.1}{10^{-4}}\approx5.9$ b) Here $M=5.8$. Thus $I=S10^M=10^{-4}(10^{5.8})\approx63 $ cm