Answer to Question #174430 in Algebra for mariah Perez

Question

A formula for calculating the magnitude of an earthquake is M=2

3

log(E

E

)

 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.

 

Round to the nearest hundredth.

 

The magnitude of the second earthquake was ???

Answer 1

The MMS is given by the following equation,

$M=23log_{10}(EE_o)$

when M=3.9

$3.9=23log_{10}(EE_o) \\$

${3.9\over23}=log_{10}(EE_o)$

${0.17}=log_{10}(EE_o)$

$EE_o=10^{0.17}=1.48$ ...........(1)

now when energy becomes 800 times, the M is given by,

$M=23log_{10}(800EE_o)\\=23log(800*1.48)\\ =23*3.07\\ =70.68$

hence second earthquake is of 70.68 magnitude.