Question

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. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?
A.M=logI/10S
B.M=log(10S)
(It was C i just turned it in)
C.M=log10S/S
D.M=log10/S

Answer 1

Answer:

C: M = log(10S/S)

Step-by-step explanation:

We know that 'I' is the intensity of the earthquake based on its wave amplitude and S is the magnitude of a standard earthquake.

If we want to calculate the magnitude of an earthquake that is 10 times bigger than the standard one then we do the following operation:

I = 10S (i) (because the intensity is 10 times that of the standard earthquake)

Now:

M = log (I / S) (ii)

Replace (i) in (ii)

M = log (10S / S)

Finally, the correct answer is option C

Answer 2

Answer:

The required equation is $M=\log \frac{10S}{S}$ i.e. M = 1.

Step-by-step explanation:

We are given that,

Magnitude of an earthquake is defined as $M=\log \frac{I}{S}$,

where I is the intensity of the earthquake measured on seismograph and S is the intensity of the standard earthquake.

Since, it is given that,

The intensity of an earthquake measured is 10 times more than that of the standard earthquake.

i.e. I = 10S

So, we get,

Magnitude of an earthquake is $M=\log \frac{10S}{S}$,

i.e. Magnitude of an earthquake is $M=\log 10$,

i.e. Magnitude of an earthquake is M = 1.

Hence, the required equation is $M=\log \frac{10S}{S}$ i.e. M = 1.