9. Natural Logs, Change of Base, Richter Scale

Page 9 #1

Go to Desmos. Type in logs with different bases. Try negative numbers, 0, and positive numbers. Then answer the question.

What bases can be used with logarithms

Page 10 #5a

Use the definition of the natural logarithm function, as well as properties of logarithms, to simplify or expand each expression.

$$\ln e=$$

Hint: type into Desmos if you are not sure

Page 10 #5b

Use the definition of the natural logarithm function, as well as properties of logarithms, to simplify or expand each expression.

$$\ln e^2=$$

Use properties of logarithms

Page 10 #5c

Use the definition of the natural logarithm function, as well as properties of logarithms, to simplify or expand each expression.

$$\ln\left(2e^3\right)=$$

Use properties of logarithms

Page 10 #5d

Use the definition of the natural logarithm function, as well as properties of logarithms, to simplify or expand each expression.

$$\ln\left(\left(2e\right)^3\right)=$$

Use properties of logarithms

Page 10 #7b

Use the Change of Base Property to evaluate the following logarithms. Then use Desmos to verify.

$$\log_29=$$

Page 11 #7c

Use the Change of Base Property to evaluate the following logarithms. Then use Desmos to verify.

$$\log_{1000}100=$$

Page 11 #7d

Use the Change of Base Property to evaluate the following logarithms. Then use Desmos to verify.

$$\log_5200=$$

Which scale measures the magnitude, or size, of an earthquake?

The strength of the shaking from an earthquake is called it's intensity.

Choose the richter scale numbers that would indicate a major earthquake causing serious damage.

Page 11 #14

There was an event that had a relative intensity of 989. Given that a heavy truck rumbling by can cause a microquake with a Richter rating of 3 or 3.5, and "moderate" quakes have a Richter rating of 4 or more, what was likely the event that occurred?