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Determine the magnitude of an earthquake if its energy in ergs is $3.23 \times 10^{19}$.

$$5.1$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:05

Determine the magnitude of…

01:02

01:03

00:57

Determine the energy of an…

One of the strongest recor…

02:06

EARTHQUAKES Anchorage, Ala…

01:09

01:06

01:10

Anchorage, Alaska, had a m…

02:26

00:58

The magnitude $M$ of an ea…

Using the information given to us that the energy of an earthquake is 3.32 times 10 to the power of 19. We want to find what is its magnitude. We're going to be using the function written in green here, which is this function relating energy and magnitude on the Richter scale. Start by plugging this information in. So on this left hand side we've got the log of our energy. So 3.23 Times 10 to the 19th Equal to 11.8 Plus 1.5 M. Start by simplifying the left hand side, which gives us 19.5092 Equal to 11.8 plus 1.5 M. We need to subtract 11.8 from both sides giving us 7.7092 is equal to 1.5 M. And now dividing both sides by that 1.5 simplifies down to em or otherwise giving us our magnitude of this earthquake, which is equal to 5.2

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