Question

Check my answer? Will give medal!
On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?

Answer 1

\[M=\log(\frac{ l }{ l _{0} })\]
M = the magnitude of an earthquake
I = the intensity of an earthquake
I0 = the smallest seismic activity that can be measured

Answer 2

0.40
1.02
1.05
2.51

Answer 3

I believe it's 2.51, but I can't really word how exactly I got the answer so that my process makes sense. If anyone can help me out with an actual explanation and check the answer I've given, I would greatly appreciate it.

Answer 4

hello, would you like help?

Answer 5

Sure. Why not. :)

Answer 6

On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?

Let
M1 = magnitude of first earthquake
M2 = magnitude of second earthquake
I1 = intensity of first earthquake
I2 = intensity of second earthquake
Io = intensity of the smallest seismic activity that can be measured
which is unknown to us, but which is a constant.

M1 = log ( I1 / Io)

M2 = log ( I2 / Io)

Answer 7

I've kinda forgotten how to do this. How would you calculate the intensity to compare the two?

Answer 8

you can substitute and use properties of logs

Answer 9

We are given that
M1 = 8.6
M2 = 8.2

substitute

8.6 = log( I1 / Io)
8.2 = log (I2 / Io)

raise both sides to the power of 10


10^8.6 = 10^log(I1 / Io)
10^8.2 = 10^log(I2 / I0 )

Answer 10

now 10^log(anything) = anything

they cancel

Answer 11

10^log(I1 / Io) would now just be I1 / Io
and 10^log(I2 / Io) would be I2 / Io

Answer 12

8.6 = log( I1 / Io)
8.2 = log (I2 / Io)

raise both sides to the power of 10


10^8.6 = 10^log(I1 / Io)
10^8.2 = 10^log(I2 / Io)


10^8.6 = I1 /Io
10^8.2 = I2 / Io


multiply both sides by Io

10^8.6 * Io = I1

10^8.2 * Io = I2


I2 / I1 = (10^8.6 * Io) / (10^8.2 * Io)

Answer 13

now on the right side, the Io's cancel . remember its a constant

Answer 14

I2 / I1 = (10^8.6 * Io) / (10^8.2 * Io)
= 10^8.6 / 10^8.2
= 10 ^ (8.6 - 8.2)
= 10^.4 = 2.51

Answer 15

the reason why i divided I2 / I1, was because the question asked by what approximate factor is the intensity of earthquake 1 greater than earthquake 2

Answer 16

Wow! So I was right? I don't even remember how I got it.

Answer 17

Thank you for your help!

Answer 18

:)

Answer 19

now you can close this month long question :)

Answer 20

oh you did