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Determine the energy of an earthquake if its magnitude is 7.3.

$$5.62 \times 10^{22} \text { ergs }$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Oregon State University

McMaster University

Harvey Mudd College

Lectures

01:06

Determine the energy of an…

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00:57

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01:02

Determine the magnitude of…

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03:38

On September $25,2003,$ an…

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One earthquake has magnitu…

01:31

The magnitude $M$ of an ea…

Given an earthquake magnitude equal to 7.3. What is its energy level? So we're going to be using this function written in green. And let's start by plugging in the information that we do have. So the left hand side is still the log of energy. We don't know what that is quite yet. We have 11.8 plus 1.5 times or magnitude which is 7.3. Go ahead and solve for that right hand side, which leaves us with the log of E is equal to 22.75. Now here it helps to write this in exponential form. So we then see that E is equal to 10 to the power of 22.75, Calculating that. And then rewriting it in scientific notation will give us that energy level of this earthquake which is 5.62 Times 10 to the power of 22 er eggs. So that is our energy of this earthquake given its magnitude equaling 7.3.

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