Chapter 4, Exponential and Logarithmic Functions - Section 4.7 - Logarithmic Scales - 4.7 Exercises - Page 421: 9

a) $5.49$ b) $6.3$ cm

We know that $M=\log\frac{I}{S}$ and thus $10^M=\frac{I}{S}$ a) Hence, here if $I=31.25$, we have: $M=\log\frac{31.25}{10^{-4}}\approx5.49$ b) Here $M=4.8$. Thus, $I=S10^M=10^{-4}(10^{4.8})\approx6.3 $ cm