Unit 8 Review | Logs and Exponentials

Unit 8 Review | Logs and Exponentials

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Topics

• Lesson 8.1 | Graphing Logs & Exp

• Lesson 8.2 | Properties of Logs

• Lesson 8.3 | Solving Logs

• Lesson 8.4 | Solving Exps

• Lesson 8.5 | Natural Logs

• Lesson 8.6 | Applications

Exponential Functions

Include a HORIZONTAL asymptote

Focus on the KEY POINTS!

This will help you find transformations.

Multiple Select

Identify the transformations.

• Flip on x-axis

• Left 1

• Left 2

• Down 4

• Down 5

What are the transformations?

Moved DOWN 5 (new HA!)
Moved LEFT 2
Flipped x-axis

 $y=-\left(3\right)^{x+2}-5$  

Logarithm Functions

Include a VERTICAL asymptote

Multiple Select

Identify the transformations.

• Flip y-axis

• Flip x-axis

• Moved left 5

• Moved left 4

• Down 6

Transformations?

Flip x-axis

LEFT 5

Down 6

 $y=-\log_4\left(x+5\right)-6$  

Multiple Choice

Which function in shown?

• Logarithm

• Exponential

Multiple Choice

Which function in shown?

• Logarithm

• Exponential

Multiple Choice

Which function in shown?

• Logarithm

• Exponential

Multiple Choice

Where would the asymptote be for this graph?

• y = 4
• y = -4
• x = 3
• x = -3

Multiple Choice

What equation matches the graph?

• f(x) = 3^x
• f(x) = (⅓)^x
• f(x) = log₃(x)

Multiple Choice

Which graph has a horizontal asymptote?

• Exponential

• Logarithmic

• Both

How can we rewrite logs into exponentials?

This shortcut may help!

We also have used

"swoop-de-loop!"

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Multiple Choice

Rewrite as an exponential:
log(10,000)=4.

• e⁴=10,000
• 4^10,000=10
• 10⁴=10,000
• 0⁴=10

Multiple Select

Rewrite as a LOGARITHM
 $e^{\left(x+1\right)}=5$  

Select all that work!

•  $\ln5=x+1$  

•  $\log_e5=x+1$  

•  $\ln_e5=x+1$  

•  $\log5=x+1$  

Multiple Choice

 $\ln\left(\frac{2x^2y}{z^4}\right)$  

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz

Multiple Choice

Expand as much as possible:

log₄x²

• log₄ + logx²

• log4/logx²

• log₄x²

• 2log₄x

Multiple Choice

Rewrite as a single log:

log 5 + log 7 + 3

• $\log15$

• $\log35+3$

• $\log38$
  

• Not here

Multiple Select

Which of the following would be a CORRECT expanded form? $\log_3\left(\frac{27a^4}{3c}\right)$  
Select all!

•  $\log_327+4\log_3a-\log_3\left(3c\right)$  

•  $2+4\log_3a-\log_3c$  

•  $\log_39+4\log_3a-\log_3c$  

•  $\log_327+4\log_3a-\log_33+\log_3c$  

Multiple Choice

Solve for x.
 $3^{x-4}=5$  

•  $\log_35+4$  

•  $\log_39=2$  

•  $\log_53+4$  

•  $\log_35-4$  

Multiple Choice

The value of an iPhone depreciates each year. You purchase your phone for $799 and when you trade it in 2 years, it is now $345.

How much did it lose value each year?

• About 34.29%

• About 65.71%

• About 17.46%

• About "not here"%

Multiple Choice

You want to invest a some money in an account that will compound continuously for 25 years at 3.85% interest.

If you have $24,500 in your account, what did you initially deposit?

• Around $9357.45

• About $3875.45

• Around $64146.73

• Around $10165.21

Multiple Choice

Moo!!!! Half-life of calcium is 163 days.

How long will it take for 305mg of calcium to drop to 10%?

• 541.47 days

• 4.61 days

• 1320.41 days

• "Not here" days