The formula 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.

An earthquake with a magnitude of 8 is 100 times stronger than an earthquake with a magnitude of 6.

Given the following data:

To determine how many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6:

Mathematically, the magnitude of an earthquake is given by the formula:

Where:

For earthquake A:

For earthquake B:

For strength:

Strength = 100

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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.

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step-by-step explanation:

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