The intensity levels I of two earthquakes measured on a seismograph can be compared by formula: log I1/I2 = M1 - M2
where M is the magnitude given by the Richter Scale. In August 2009, an earthquake of magnitude 6.1 hit Honshu, Japan. On 31 January 1906, Ecuador coast, was hit with a more devastating earthquake, this time with a magnitude of 8.8.
To the nearest whole number, how many times greater was the intensity of the 31 January 1906 earthquake?
May someone help me set this problem up. I'm just struggling with what goes in for the I's and for the M's is it just the 6.1 and 8.8? Idk this problem is confusing me.
I appreciate any help.
Sure, I can help you set up the problem!
In the formula log I1/I2 = M1 - M2, I1 and I2 represent the intensity levels of the earthquakes, and M1 and M2 represent the magnitudes of the earthquakes.
In this case, we want to compare the intensity of the earthquake in Honshu, Japan (6.1 magnitude) to the intensity of the earthquake on the Ecuador coast (8.8 magnitude).
To find the answer, we need to substitute the magnitudes into the formula and calculate the ratio of intensities.
Let's label the earthquake in Honshu, Japan as earthquake 1 (E1) and the earthquake on the Ecuador coast as earthquake 2 (E2).
So we have:
M1 = 6.1 (magnitude of E1)
M2 = 8.8 (magnitude of E2)
Now let's substitute these values into the formula:
log(I1/I2) = M1 - M2
log(I1/I2) = 6.1 - 8.8
To find the ratio of intensity, we need to calculate 10 to the power of each side of the equation. This will cancel out the logarithm and give us the ratio directly.
So the equation becomes:
10^(log(I1/I2)) = 10^(6.1-8.8)
The left side of the equation simplifies to just I1/I2:
I1/I2 = 10^(-2.7)
Now, calculate 10^(-2.7) using a calculator or any other method, and the result will give you the ratio of the intensities.
To the nearest whole number, you can round the final answer.
I hope this helps you set up the problem correctly! Let me know if you have any other questions.
yes, just take the log of the quotient.
I1/I2 = 10^(M1-M2)