Answer to Question #158197 in Algebra for Jake

Question

A formula for calculating the magnitude of an earthquake is M=2/3log(EE0)

 that uses the common (base 10) logarithm. This is called the Moment Magnitude Scale (MMS), an alternative to the more well known Richter Scale. One earthquake has magnitude 3.9

 on the MMS. If a second earthquake has 800

 times as much energy as the first, find the magnitude of the second quake.

 

Answer 1

$M= \frac{2}{3log(EE')}$

when M= 3.9,

3.9= $\frac {2}{3log(EE')}$ [ log (base 10) is used ]

log(EE')= $\frac{2}{3*3.9}$

log(EE')= 0.171

EE'= 10^0.171 =1.482

when energy became 800 times as much as energy as first earthquake had, then

$M= \frac{2}{3log(800*1.482)}$

$M= \frac{2}{3*3.074}\\M= 0.217$

hence, the magnitude of second earthquake is M= 0.217