9. Natural Logs, Change of Base, Richter Scale

Natural Logs, Change of Base, and Richter Scale

​Page 9-11

Multiple Choice

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

• All numbers

• Any negative number

• Any positive number

• Any positive numbers except 1

• Any positive number and 0

Open Ended

Page 9 #2

How are logarithms with base e used in science?

HINT: look this up if you don't know

Page 9 #4

Multiple Choice

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

• e

• 0

• 1

Multiple Select

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

• 1

• $$2\ln e$$

• $$\ln e$$

• 2

• $$\ln e\ln e$$

Multiple Select

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

• $$\ln5e$$

• $$\ln2+3\ln e$$

• $$\ln2+\ln e^3$$

• $$\ln6e$$

Multiple Select

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

• $$\ln2^3+\ln e^3$$

• $$3\ln2+3\ln e$$

• $$3\ln2+\ln3e$$

• $$6\ln2e$$

Labelling

Page 10 #6

What are the two bases used most often for logarithms? What are the common names for these logarithms?

Drag labels to their correct position on the image

2

natural logarithm

common logarithm

1

10

0

regular logarithm

Change of Base Formula

​Page 10 #7

​Type into Desmos

Multiple Select

Page 10 #7b

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

$$\log_29=$$

• $$\frac{\log2}{\log9}$$

• $$\frac{\log9}{\log2}$$

• 0.3154

• 3.1699

Multiple Select

Page 11 #7c

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

$$\log_{1000}100=$$

• $$\frac{\log100}{\log1000}$$

• $$\frac{\log1000}{\log100}$$

• 1.5

• 0.6667

Multiple Select

Page 11 #7d

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

$$\log_5200=$$

• $$\frac{\log5}{\log200}$$

• $$\frac{\log200}{\log5}$$

• 3.292

• 0.3037

​

Earthquakes

• Richter scale measures the magnitude, size, intensity of an earthquake

• Every number increase represents a 10-fold increase in intensification.

Multiple Choice

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

• Mercalli

• Richter

• weight

• density

Multiple Choice

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

• True

• False

Multiple Choice

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

• 1.0-3.5

• 7.0-7.9+

• In the 100s

• Under 6.0

Multiple Select

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?

• 3

• 4

• Heavy Truck Rumbling

• Moderate Earthquake

Page 11 #16
Try on your own. I will go over these after

​False

Page 11 #17

​Complete this side on your own

Copy this down

An earthquake that measures R=5 on the Richter Scale is how many times as intense as an earthquake that measures R=3?