Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 534: 13

$M=9.7$

$S=10^{-4}$cm $I=500,000cm=5\times10^5$ Putting in the formula $M=\log \frac{I}{S}$ $M=\log \frac{5\times10^5}{ 10^{-4}}$ $M=\log( 5\times10^5\times10^4)$ $M=\log( 5\times10^5\times10^4)$ $M=\log( 5\times10^{5+4})$ $M=\log( 5\times10^9)$ $M=\log 5+\log 10^9$ $M=\log 5+9\log 10$ $M=\log 5+9$ $M=0.6989+9$ $M=9.6989$ $M=9.7$ Correct to two significant digits