Question

the relationship between the relative size of an earthquake, S, and the measure of the earthquake on the Richter scale, R, is given by the equation log S = R. If an earthquake measured 3.2 on the Richter scale, what was it relative size? Express your answer to the nearest hundredth

Answer 1

Relative Size, S, is 1584.89

Explanation:

The equation is
`R=log_(10)(S)`

Where,

• R is the measurement in Richter Scale
• S is the relative size of the earthquare

It is given that in Richter Scale, an earthquake measured 3.2, so
`R=3.2`.

They want to know relative size, S, so we put given information in equation and solve for S:

`R=log_(10)(S)\\3.2=log_(10)(S)`

Converting to exponential form, we have:

`3.2=log_(10)(S)\\S=10^(3.2)\\S=1584.8932`

Rounding to nearest hundredth, we have:

`S=1584.89`