SOLUTION: The magnitude of an earthquake is measured on the Richter scale as a logarithm of the intensity of the shock wave. For magnitude R and intensity I, the formula is R=log(I) The Sep

Algebra ->  Human-and-algebraic-language -> SOLUTION: The magnitude of an earthquake is measured on the Richter scale as a logarithm of the intensity of the shock wave. For magnitude R and intensity I, the formula is R=log(I) The Sep      Log On


   

Question 1143308: The magnitude of an earthquake is measured on the Richter scale as a logarithm of the intensity of the shock wave. For magnitude R and intensity I, the formula is R=log(I) The September 20, 1999 earthquake in Taiwan measured 7.7 on the Richter scale. The San Jacinto earthquake in October 31, 2001 measured 5.1 on the scale. How many times more intense was the Taiwan earthquake than the San Jacinto earthquake? Round your answer to two decimal places, if necessary.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula is r = log(i)

by the laws of logarithms, this is true if and only if i = 10^r.

when r = 7.7, the formula becomes 7.7 = log(i).

this is true if and only if 10^7.7 = i.

this makes i = 50118723.36272725

likewise, when r = 5.1, i = 10^5.1 = 125892.541179417

the intensity of the earthquake that is 7.7 on the richter scale is 10^7.7 / 10^5.1 = 398.107170553 times AS intense.

how many times MORE intense would be (10^7.7 - 10^5.1) / 10^5.1 = 397.107170553

round that to two decimal places and it becomes 397.11 times MORE intense.