Basic Logarithmic Properties

Unit 4: Exponential Functions

4.4 More Properties of Logarithms

Open Ended

What do you think is the value of x if $$\ln\ e^x=4$$ ?

Multiple Choice

Solve for x if lnx=0.

• e

• 1

• x

• 3

Multiple Choice

Solve for y if $$\ln\ y=\ \ln3$$

• e

• 2/3

• 3

• -3

Part 1:Expanding and Condensing Logarithms

Logarithms are a little weird because they can be expanded and condensed. Depending on the problem, you may need to do both in order to solve logarithmic equations.

The properties we are going over today can be used to expand or condense an expression, depending on the problem.

1. Product Property

Multiple Choice

Condense the logarithm:

$$\log3\ +\ \log7$$  

• log 10

• log 21

• log 3/7

• log 3/log 7

Multiple Choice

Expand log_b(xy).

• log_bx+log_by

• log_bx-log_by

• log_bx*log_by

• log_bx/log_by

2. Quotient Property

Multiple Choice

Write log_b(x/y) as two logs

• log_bx-log_by

• log_bx+log_by

• log_bx*log_by

• log_bx/log_by

3. Power Property

​mm

Multiple Choice

Expand log_b(xⁿ)

• nlog_bx

• (log_bx)ⁿ

• xⁿlog_bx

• log_b(xⁿ)

Multiple Choice

Use the properties of logarithms to expand te logarithm

• A

• B

• C

• D

Multiple Choice

Which of the logarithms below is equivalent to the following: $$2\log12$$  

• log 10

• log 6

• log 24

• log 144

Part 2: Change of Base

Open Ended

When using logarithmic properties, certian operations are connecter, or paired, together. An example would be multiplication and addition. What other operations are paired together?

Multiple Choice

Which property of logarithms is demonstrated below: 

$$\log_920\ =\ \frac{\log20}{\log9}$$  

• Product property

• Quotient property

• Power property

• Change of Base Property

Multiple Choice

Use the change of base property to rewrite as a single logarithm: $$\frac{\log15}{\log3}$$  

• $$\log\ \frac{1}{5}$$  

• $$\log5$$  

• $$\log_{15}3$$  

• $$\log_315$$