SOLUTION: M= log(E) - 11.8 / 1.5 26 1. A large earthquake is one that releases 10 ergs of energy. What is the magnitude (to the nearest hundredth) of such an earthqu

Question 1196929: M= log(E) - 11.8 / 1.5 26
1. A large earthquake is one that releases 10 ergs of energy. What is the magnitude (to the nearest hundredth) of such an earthquake on the Richter scale?
2. How much energy (in ergs) is released in an 7.0 earthquake? ?
10 ergs
Thanks!

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your formula states that:
M = log(E) - 11.8 / 1.5
since log(E) = log(10^26) = 26, the formula becomes:
M = 26 - 11.8 / 1.5
that becomes:
M = 18.13 which is unreasonable, since the richter scale doesn't go up that far.
i believe the formula should be:
M = (log(E) - 11.8) / 1.5
the log(E) - 11.8 needs to be in parentheses to show that the whole expression is in the numerator.
the formula then becomes:
M = (26 - 11.8) / 1.5 = 9.466666......
round to two decimal places to get M = 9.47
that looks more reasonable.
from M = (log(E) - 11.8) / 1.5, solve for log(E) to get:
log(E) = 11.8 + 1.5 * M
when M = 7, the formula becomes:
log(E) = 11.8 + 1.5 * 7 which becomes:
log(E) = 22.3
this is true if and only if E = 10^22.3

your first answer is M = 9.47 rounded to 2 decimal places.
your second answer is E = 10^22.3

let me know if you have any questions.
theo

RELATED QUESTIONS
The equation used to relate the energy and the magnitude(M) of an earthquake is:... (answered by josmiceli)

Supposed that an earthquake released 10^6 joules of energy.What is the magnitude on a... (answered by CPhill)

B. The strength of an earthquake is calculated using Richter's formula M= log (A/10^-6)... (answered by Theo)

When measuring the intensity of an earthquake, a seismometer is used 100km away from the... (answered by Boreal)

The earthquake with a magnitude 8 releases a million times more energy than an earthquake (answered by Theo)

The kinetic energy, K, of a moving particle acted on by various forces depends... (answered by ankor@dixie-net.com)

To find the energy of Earthquakes (measured in Joules) scientists use the equation: E =... (answered by stanbon)

Earthquake intensity, I, is given by the equation I=Io(10)^m, where m is the magnitude... (answered by Fombitz)

The magnitude R of an earthquake is given by R = log +40 Where E (in joules) is the... (answered by math_tutor2020)