Answer
a. 5.494
b. 6.31 cm
Work Step by Step
Given the magnitude equation $M = \log \frac{I}{S}$
with $S = 10^-4$ and $I = 31.25$
a. Solve for M
$M = \log \frac{31.25}{10^{-4}}$
$M = \log 31.25 + \log 10^{4} = 5.494$
b. Given M = 4.8, find the intensity
$4.8 = \log \frac{I}{10^{-4}}$
$10^{4.8} = \frac{I}{10^{-4}}$
$I = 10^{0.8} = 6.31 cm$