Question

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function M(x) = log , where x0 = 10-3.

Two earthquakes differ by 0.1 when measured on the Richter scale. How would the seismographic readings differ at a distance of 100 kilometers from the epicenter?

Answer 1

please give the function M(x) properly.

Answer 2

m(x)=log(x/x0)

Answer 3

x0=10^-3

Answer 4

ok,so let the 2 readings be x1 and x2
So M(x1)-M(x2)=0.1
so log(x1/x0)-log(x2/x0)=0.1
ok till here ?

Answer 5

yes

Answer 6

so using log properties:
log A-log B =log (A/B)
we get log(x1/x2)= 0.1 (x0 gets cancelled)
ok?
so
x1/x2 = 10^(0.1)

Answer 7

so using log properties:
log A-log B =log (A/B)
we get log(x1/x2)= 0.1 (x0 gets cancelled)
ok?
so
x1/x2 = 10^(0.1)

Answer 8

yessss i get it :P

Answer 9

so 10^0.1=1.259
so they will differ by 1.259.