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Determine the magnitude of an earthquake if its energy in ergs is $4.59 \times 10^{18}$.

$$4.6$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

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Let's find the magnitude of an earthquake whose energy is 4.59 times 10 to the 18th. Using this function over here. So to start, we've got the log of our energy. We're just plugging this in. The value that was given to us a 4.59 times 10 to the 18th Is equal to 11.8 plus 1.5 M. Start by simplifying the left hand side, which gives us six gives us 18 .6618, Which is equal to 11.8 plus 1.5 M. Now we can subtract 11.8 from both sides to continue simplifying, which gives us 6.8618 on the left hand side Equal to 1.5 M. And I would need to divide both sides by 1.5. And by doing that, we see that this earthquake has a magnitude equal to 4.6.

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