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The magnitude, [tex][tex]$M$[/tex][/tex], of an earthquake is defined to be [tex][tex]$M = \log \left( \frac{I}{S} \right)$[/tex][/tex], where [tex][tex]$I$[/tex][/tex] is the intensity of the earthquake (measured as the amplitude of the seismograph wave) and [tex][tex]$S$[/tex][/tex] is the intensity of a "standard" earthquake, which is barely detectable.

Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?

A. [tex][tex]$M = \log \left( \frac{I}{10 S} \right)$[/tex][/tex]
B. [tex][tex]$M = \log (10 S)$[/tex][/tex]
C. [tex][tex]$M = \log \left( \frac{I}{S} \right)$[/tex][/tex]
D. [tex][tex]$M = \log \left( \frac{10 I}{S} \right)$[/tex][/tex]

Sagot :

GinnyAnsweridn
To determine the correct equation for the magnitude of an earthquake that is 10 times more intense than a standard earthquake, let's use the formula for the magnitude of an earthquake:

[tex]\[ M = \log \left( \frac{I}{S} \right) \][/tex]

Where:

- [tex]\( M \)[/tex] is the magnitude.
- [tex]\( I \)[/tex] is the intensity of the earthquake.
- [tex]\( S \)[/tex] is the intensity of a "standard" earthquake.

Given that the intensity [tex]\( I \)[/tex] of the earthquake is 10 times the intensity of a standard earthquake [tex]\( S \)[/tex], we can write:

[tex]\[ I = 10S \][/tex]

Using the formula for the magnitude:

[tex]\[ M = \log \left( \frac{I}{S} \right) \][/tex]

Substitute [tex]\( I = 10S \)[/tex]:

[tex]\[ M = \log \left( \frac{10S}{S} \right) \][/tex]

Simplify the fraction:

[tex]\[ M = \log (10) \][/tex]

Therefore, the equation that represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake is:

[tex]\[ M = \log (10) \][/tex]

Hence, the answer is not among the provided options. However, if we consider the provided options, the closest interpretation could be:

[tex]\[ M = \log (10S) \][/tex]

Although this is not a perfect match to our simplified equation, it is the closest representation among the four choices given. Thus, the best matching answer among the provided options would be:

[tex]\[ M = \log (10S) \][/tex]
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