Logarithmic Scale Calculation | Ritcher Scale Homework Example

[Macleef]

Homework Statement

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Homework Equations

M = log(I_i / I_o)

The Attempt at a Solution

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[wildman]

No, no... you are making it far too complicated.

What is [tex] I_X [/tex] in terms of [tex] I_E [/tex] ? In other words, what number do you have to multiply [tex] I_E [/tex] by to get [tex] I_X [/tex]?
Then get rid of [tex] I_X [/tex] in your equation.
Finally think about what multiplication inside of a log function maps to on the outside. I'll give you a clue on the last one and it is +.

 

[Architeuthis Dux]

I would like to clarify that the equation provided is actually the equation for calculating the magnitude of an earthquake using the Richter scale, not a logarithmic scale in general. The Richter scale is a logarithmic scale used to measure the strength or magnitude of an earthquake, with each increase in magnitude representing a tenfold increase in the amplitude of the seismic waves. The equation provided is a simplified version of the original Richter scale equation, which takes into account the intensity of the earthquake at a certain distance from the epicenter (I_i) compared to a standard intensity level (I_o). This equation allows scientists to quickly and easily calculate the magnitude of an earthquake based on the intensity measurements. It is important to note that the Richter scale is not an absolute scale, as different magnitudes can be obtained depending on the distance from the epicenter and the type of seismic waves produced. Despite its limitations, the Richter scale remains a widely used and recognized method for measuring earthquake magnitude.