+0

# Logarithm Word Problem

0
52
2
+52

In January, the Richter scale measured an earthquake of magnitude 3.2. A month later, in February, you hear on the news that there has been another earthquake, which is 27 times more intense than the one in January. What is the magnitude of the second earthquake?

UpTheChels  Oct 28, 2017
Sort:

#1
+1

Go online to this USGS site which explains the difference between "intensity" and "magnitude" of an earthquake.  https://earthquake.usgs.gov/learn/topics/mag_vs_int.php

Guest Oct 28, 2017
#2
+2

Use this formula to find the Magnitude of the earthquake:

E=10^[1.5M + 4.8], where E=Equivalent Energy, M=Richter Scale Magnitude.

E=10^[1.5*3.2 + 4.8]

E=10^[4.8 + 4.8]

E=10^[9.6]

E=3,981,071,705.5 Joules - energy-equivalent of 3.2 magnitude earthquake.

3,981,071,705.5 x 27 =10^[(1.5*M) + 4.8], solve for M

1.07489×10^11 = 10^(1.5 M + 4.8)

1.07489×10^11 = 10^(1.5 M + 4.8) is equivalent to 10^(1.5 M + 4.8) = 1.07489×10^11:
10^(1.5 M + 4.8) = 1.07489×10^11

Take the logarithm base 10 of both sides:
1.5 M + 4.8 = 11.0314

Subtract 4.8 from both sides:
1.5 M = 6.23136

Divide both sides by 1.5:
M = 4.15424 - The magnitude of an earthquake 27 times the intensity of 3.2 magnitude.

Guest Oct 28, 2017

### 24 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details