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# A nice word problem

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The magnitude  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 that caused only minor damage. How many times more intense was the San Francisco earthquake than the South American one?

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 $$I_{0}$$.

Sloan  Jun 7, 2018

#1
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log property to use here is logb(x) = y becomes by = x

10^M = I/I0

I = (I0 * 10^m)

we know m= 8.3 for san fran

we know m= 4 for south amer

(10^8.3 * I0 )

____________  = 19952.62 times as intense.

(10^4 * I0)

Guest Jun 7, 2018
#1
+1

log property to use here is logb(x) = y becomes by = x

10^M = I/I0

I = (I0 * 10^m)

we know m= 8.3 for san fran

we know m= 4 for south amer

(10^8.3 * I0 )

____________  = 19952.62 times as intense.

(10^4 * I0)

Guest Jun 7, 2018