Answer to Question #134049 in Algebra for Lauren

Question

A formula for calculating the magnitude of an earthquake is M=23log(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 600 times as much energy as the first, find the magnitude of the second quake.

Answer 1

The MMS is given by equation,

M=23log$_{10}$ (EE$_o)$

when M=3.9,

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

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

$0.17=log_{10}(EE_o)$

$EE_o=10^{0.17}=1.48$ .....(1)

Now when Energy became 600 times the M is given by,

$M=23log_{10}(600EE_o)$

=23$log_{10}(600\times 1.48)$

=23$\times 2.95$

=67.81

Hence the Magnitude of the second quake is 67.81