Question

The magnitude M on the Richter scale of an earthquake as a function of its intensity I is given by $$M = \log_{10}\left(\frac{I}{I_0}\right),$$ where $$I_0$$ is some fixed reference level of intensity. The 1906 San Francisco earthquake had a magnitude of 8.3 on the Richter scale. Suppose that at the same time in South America there was an earthquake with magnitude 4.7 that caused only minor damage. How many times more intense was the San Francisco earthquake than the South American one? Answer: Hint: You don't need to know what $$I_0$$ is. Plug in the respective magnitudes and use the log properties you know to compare the resulting values for I in terms of this $$I_0$$.

Name: the magnitude m on the richter scale of an earthquake as a function of its intensity i is given by m log10leftfracii0right where i0 is some fixed reference level of intensity the 1906 san 12215
Uploaded: 2021-11-18T16:56:19-08:00
Duration: 1 min 32 s
Channel: David Mccaslin
Description: the magnitude m on the richter scale of an earthquake as a function of its intensity i is given by m log10leftfracii0right where i0 is some fixed reference level of intensity the 1906 san 12215

          The magnitude M on the Richter scale of an earthquake as a function of its intensity I is given by
$$M = \log_{10}\left(\frac{I}{I_0}\right),$$
where $$I_0$$ is some fixed reference level of intensity.
The 1906 San Francisco earthquake had a magnitude of 8.3 on the Richter scale. Suppose that at the same time in South America there was an earthquake with magnitude 4.7 that caused only minor damage. How many times more intense was the San Francisco earthquake than the South American one?
Answer:
Hint: You don't need to know what $$I_0$$ is. Plug in the respective magnitudes and use the log properties you know to compare the resulting values for I in terms of this $$I_0$$.

$the magnitude m on the richter scale of an earthquake as a function of its intensity i is given by m log10leftfracii0right where i0 is some fixed reference level of intensity the 1906 san 12215$

Added by Ramon R.

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