1. ## log question

I have a logarithm word problem that i am having problems with. not sure where to plug in the numbers and how to get my result. any help will be greatful.

it is a 2 part problem.

Measured on the richter scale, the magnitude of an earthquakes of intensity I is defined as R=log(I/I0), (that is an I with a base of 0 in the denominator) where I0 is the minimum level for comparison. a) what is the richter scale reading for an earthquake whose intensity was 83,000,000I0?
b) find the intensity I in terms of I0 of an earthquake that measured a 6.9 on the richter scale. (R=6.9)

2. Originally Posted by mamajen
I have a logarithm word problem that i am having problems with. not sure where to plug in the numbers and how to get my result. any help will be greatful.

it is a 2 part problem.

Measured on the richter scale, the magnitude of an earthquakes of intensity I is defined as R=log(I/I0), (that is an I with a base of 0 in the denominator) where I0 is the minimum level for comparison. a) what is the richter scale reading for an earthquake whose intensity was 83,000,000I0?
b) find the intensity I in terms of I0 of an earthquake that measured a 6.9 on the richter scale. (R=6.9)
You have an equation

a) $\displaystyle R = \log \left(\frac{I}{I_0}\right)$
where R the reading of the richter scale, I is the intensity of the earthquake, $\displaystyle I_0$ the base intensity.

You want to find R. You have I.

b) Now you want to find I. You have R.

You will be able to remove the log function by applying the exponential function to both sides (assuming the log = ln. Otherwise, use the base of the log instead of e)

EDIT: I thought about it for a while. The richter scale's logarithm is in base 10 because an increase of 1 on the scale is a tenfold increase in intensity. So $\displaystyle 10^{log_{10}(x)} = x$

3. the I with the base of 0 is what is throwing me off. we have been taught to use the scientific calculator. I was never taught to do any of this by hand. I don't know how to enter a base of 0 in the calc. thanks for your help

4. Originally Posted by mamajen
the I with the base of 0 is what is throwing me off. we have been taught to use the scientific calculator. I was never taught to do any of this by hand. I don't know how to enter a base of 0 in the calc. thanks for your help
I see. It's not really I base 0. It just represents the base/initial value for intensity, which is a constant.

5. Originally Posted by Gusbob
I see. It's not really I base 0. It just represents the base/initial value for intensity, which is a constant.
I am still really confused. I understand that the 83,000,000=I so when I plug it in it is.....
R=log(83,000,000/83,000,000 base 0) or am I supposed to do it this way.....
R=log(83,000,000/83,000,000(83,000,000))

6. Originally Posted by mamajen
I am still really confused. I understand that the 83,000,000=I so when I plug it in it is.....
R=log(83,000,000/83,000,000 base 0) or am I supposed to do it this way.....
R=log(83,000,000/83,000,000(83,000,000))
The intensity you're given is

83 000 000$\displaystyle I_0$ , not 83 000 000

What this is saying is that the earthquake is 83 million times more intense than the baseline.

Dividing $\displaystyle I/I_0$ you'll get 83 000 000$\displaystyle I_0 / I_0$ = 83 000 000 because the I0 cancels out.

7. Originally Posted by Gusbob
The intensity you're given is

83 000 000$\displaystyle I_0$ , not 83 000 000

What this is saying is that the earthquake is 83 million times more intense than the baseline.

Dividing $\displaystyle I/I_0$ you'll get 83 000 000$\displaystyle I_0 / I_0$ = 83 000 000 because the I0 cancels out.
ok gotcha. that cancels which leaves you with log(83,000,000)

8. Originally Posted by mamajen
ok gotcha. that cancels which leaves you with log(83,000,000)
Yes

9. this is what i have for part b.
6.9=log(83,000,000) i then put it in exponential form
83,000,000=10^6.9
and now i would take the log or ln of both sides?
am i on the right track with this?

10. Originally Posted by mamajen
this is what i have for part b.
6.9=log(83,000,000) i then put it in exponential form
83,000,000=10^6.9
and now i would take the log or ln of both sides?
am i on the right track with this?

ok so after working this out i am not on the right track.

11. Originally Posted by mamajen
this is what i have for part b.
6.9=log(83,000,000) i then put it in exponential form
83,000,000=10^6.9
and now i would take the log or ln of both sides?
am i on the right track with this?
You shouldn't substitute 83 000 000 I0 this time. Think of this as a different earthquake from part a measuring 6.9 on the richter scale.

12. Originally Posted by Gusbob
You shouldn't substitute 83 000 000 I0 this time. Think of this as a different earthquake from part a measuring 6.9 on the richter scale.
ok so this is just a guess on my part. here is what i have.
6.9=log(I/I0)
I0*6.9=log(I)

,

,

### r=log[i/io]

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