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The magnitude, M, of an earthquake is defined to be M=log I/S, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 10 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

Respuesta :

Answer:

1

Step-by-step explanation:

       Magnitude [tex]M[/tex] of an earthquake is defined as [tex]M=log\text{ }\frac{I}{S}[/tex]. Here [tex]I[/tex] is the Intensity of the earthquake and  [tex]S[/tex] is the intensity of standard earthquake.

       We have an earthquake that is 10 times more intense than a standard earthquake. Let us denote the intensity of the earthquake as [tex]I[/tex].

       10 times more intense than standard earthquake ⇒ [tex]I=10S[/tex]

   Magnitude of the earthquake = [tex]M\text{ = }log\text{ }\dfrac{I}{S}\text{ = }log\text{ }\dfrac{10S}{S}\text{ = }log\text{ }10\text{ = }log_{10}\text{ }10\text{ = }1[/tex]

∴ Magnitude of the earthquake is 1.

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