The formula M=log I/S determines the magnitude of an earthquake, where I is the intensity of the earthquake and S is the intensity of a "standard earthquake." How many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6? Show your work.

Question

Mathematics

Abdiel Everett

30 April, 16:31

The formula M=log I/S determines the magnitude of an earthquake, where I is the intensity of the earthquake and S is the intensity of a "standard earthquake." How many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6? Show your work.

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Answers (1)

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Augustus · Answer 1

100

Step-by-step explanation:

M = log (I/S)

The intensity of the first earthquake:

8 = log (I₁/S)

10⁸ = I₁/S

I₁ = 10⁸ S

The intensity of the second earthquake:

6 = log (I₂/S)

10⁶ = I₂/S

I₂ = 10⁶ S

The ratio is:

I₁/I₂ = (10⁸ S) / (10⁶ S)

I₁/I₂ = 100

It is 100 times stronger.