Math - Working with Logs!!

posted by on .

On September 26 2001, an earthquake in North Bay measured 5.0 on the Ritcher scale. What is the magnitude of an earthquake 3 times as intense as North Bay's earthquake?

I would post my answer, but in text, it's just confusing and I can't post picture links to show my work...

• Math - Working with Logs!! - ,

In 1935 C.F. Richter set up the scale of earthquakes by
R = log(I) where R is the Richter scale number and I is the intensity of the earthquake

5 = log(I)
I = 10^5

so an earthquake 3 times as intense would be 3I
so multiplying the above equation by 3
3I = 3(10^5)
log (3I) = log(3*10^5)
= log 3 + log 10^5
= .47712 + 5
= 5.47712

• Math - Working with Logs!! - ,

So, you don't use the equation:

M = log(I_i / I_o) ?

• Math - Working with Logs!! - ,

most texts, and the one that I used last, use the formula

R = log(I/I0) where 0 is a constant, the minimum intensity corresponding to R = 0

so if you want

5 = log (I/I0)
5^10 = I/I0
3*5^10 = 3I/I0
log(3*5^10 = log(I/I0)

notice it has no effect on the answer

• Math - Working with Logs!! - ,

i don't get where the 3 goes in the second line of this part :

log (3I) = log(3*10^5)
= log 3 + log 10^5

• Math - Working with Logs!! - ,

You have it right in the second line in the laws of logarithms a*b ends up equaling log 3 + log 10^5