Log Word Problem Solving - TEST - Easy Best Answer?

Question

Earthquake intensity is measured by the Richter scale. The formula for the Richter rating of a given quake is given by "R=log[I/I0]" where I0 is the "threshold quake", or movement that can barely be detected, and the intensity I is given in terms of multiples of the threshold intensity.

An earthquake was reported to have a Richter number of 5.99. How does the intensity of the earthquake approximately compare with the reference intensity?


I need to know how to solve this for a test tomorrow. First correct answer which explains how to do it gets best answer - I thought the answer was 0.77 but I was wrong.

Answer 1

You know that R = log ( I / 10 ). You wish to know the value of I if R = 5.99.

5.99 = log ( I / 10 )
10^5.99 = I / 10
( 10 ) ( 10 ^ 5.99 ) = I
10 ^ 6.99 = I

Answer 2

see this link: http://www.geo.mtu.edu/UPSeis/intensity.html

It's been a while since I worked with Richter scale equations, but I think how tou have the information written is confusing. Is the detectable level 10, 1 or something else? I think the equation of "R=log[I/I0]" isn't meant as the log of 1/10 (or 0.1) but that it covers a range of 1 to 10.

The Richter scale is a base 10 log scale with 1 being "detectable" going up to 10 (assumed to be the strongest quake). Since it's a base 10, you multiply by 10 for each number changed. I think if you start at 1.0 as the lowest you can feel, a 2.0 would be 10 times stronger, a 3.0 would be 100 times stronger (10 x 10), a 4.0 would be 1,000 times stronger (10 x 10 x 10), so a quake that's 5.99 (consider this a "6") that would be 10 x 10 x 10 x10 x10 or 100,000 times stonger than an 1.0 quake.

See if this helps with what your book gives as an answer.

Answer 3

i never took a test like that but, thinking about it, if a threshold quake can barely be detected that's like a 0.01 quake probably. so 5.99/0.01? i have no idea what I'm doing but maybe it can help