# Finding the magnitude with Logs.

• Mar 22nd 2011, 12:24 PM
JC05
Finding the magnitude with Logs.
I've been stuck on this problem for a long time now. Can someone help me? Thanks in advance :)

http://edugen.wiley.com/edugen/art2/common/pixel.gif
The magnitude of an earthquake is measured relative to the strength of a “standard” earthquake, whose seismic waves are of size W0. The magnitude, M, of an earthquake with seismic waves of size W is defined to be
http://edugen.wiley.com/edugen/share...=1300819127818.The value of M is called the Richter scale rating of the strength of an earthquake.

How many times larger are the seismic waves of the earthquake with rating of 5.7 on the Richter scale, than the seismic waves of the earthquake with a rating of 3.6 to the nearest integer.
• Mar 22nd 2011, 03:47 PM
skeeter
Quote:

Originally Posted by JC05
I've been stuck on this problem for a long time now. Can someone help me? Thanks in advance :)

http://edugen.wiley.com/edugen/art2/common/pixel.gif
The magnitude of an earthquake is measured relative to the strength of a “standard” earthquake, whose seismic waves are of size W0. The magnitude, M, of an earthquake with seismic waves of size W is defined to be
http://edugen.wiley.com/edugen/share...=1300819127818.The value of M is called the Richter scale rating of the strength of an earthquake.

How many times larger are the seismic waves of the earthquake with rating of 5.7 on the Richter scale, than the seismic waves of the earthquake with a rating of 3.6 to the nearest integer.

let the intensity of the 5.7 quake = $W_1$ , intensity of the 3.6 quake = $W_2$

$5.7 = \log\left(\dfrac{W_1}{W_0}\right)$

$3.6 = \log\left(\dfrac{W_2}{W_0}\right)$

take the difference between the two equations ...

$2.1 = \log\left(\dfrac{W_1}{W_0}\right) - \log\left(\dfrac{W_2}{W_0}\right)$

use the difference property of logarithms ...

$2.1 = \log\left(\dfrac{W_1}{W_2}\right)$

change to an exponential equation ...

$\dfrac{W_1}{W_2} = 10^{2.1} \approx 126$ times greater