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Logarithmic Functions

arl2267

New member
Nov 6, 2012
15
The magnitude of an earthquake, measured on the Richter scale, is given by

R(I)= log(I/I0)

Where I is the amplitude registered on a seismograph located 100km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale ratings of earthquakes with the following amplitudes:

a) 1,000,000I0

b) 1,000,000,000I0

Okay so would the solution be

log(100/1,000,000)= -4

log(100/1,000,000,000)= -6

???
 

SuperSonic4

Well-known member
MHB Math Helper
Mar 1, 2012
249
The magnitude of an earthquake, measured on the Richter scale, is given by

R(I)= log(I/I0)

Where I is the amplitude registered on a seismograph located 100km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale ratings of earthquakes with the following amplitudes:

a) 1,000,000I0

b) 1,000,000,000I0

Okay so would the solution be

log(100/1,000,000)= -4

log(100/1,000,000,000)= -6

???
The value of 100km is meaningless in this context - ignore it. The question is giving you values of $I$ in terms of $I_0$ which means the latter will cancel out giving a number.

Your values should be positive. If you consider it logically an earthquake 1 million times stronger than a reference will be larger on the Richter scale than said reference quake.