Logarithm Test Review

​Logarithm Test

Review​

Graphing & Solving Logarithms​

Multiple Choice

Logarithms and Exponentials are what?

• parallel
• perpendiular 
• inverses
• congurent

​First Up: Graphing Logarithms

Multiple Choice

What is the transformation of the logarithmic function $$f\left(x\right)=\log\ \left(x+3\right)-1$$  

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

Multiple Choice

Where is the vertical asymptote and what is the domain of this graph?

• asymptote x = 1 and domain

  (1, $$\infty$$  )

• asymptote y = 1 and domain

  (-1, $$\infty$$  )

• asymptote x = -1 and domain

  ( $$\infty$$ , 1)

• asymptote y = -1 and domain

  ( $$\infty$$ , 1)

Multiple Choice

find the asymptote: y = log(x+3)+2

• x=-3

• x=3

• x=-2

• x=2

Multiple Choice

Describe range of the function shown: y=log₂(x+1)

• (-∞,∞)

• (-1,∞)

• (-1,3)

• (∞, -1)

Multiple Choice

What are the transformations for the graph of ? $$y=\log_4\left(x-1\right)+5$$  

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

Multiple Choice

Where is the asymptote?

• x = 1

• y = 1

• x = -1

• y = -1

Multiple Choice

What is the vertical asymptote of the equation  $$y=\log_5\left(x+3\right)+5$$  

• x = -3

• y = -3

• x = 5 

• y = 5

Multiple Choice

What is the range of the graph  $$y=\log_2\left(x-1\right)+3$$  

• (-∞, ∞)

• [-∞, ∞]

• [0, ∞)

• (0, ∞)

Match

Match the following functions with their asymptote

• $$\log\left(x+2\right)-3$$  

• $$\log\left(x+3\right)-2$$  

• $$\log\left(x-2\right)+3$$  

• $$\log\left(x-3\right)-3$$  

x = -2

x = -3

x = 2

x = 3

• x = -2

• x = -3

• x = 2

• x = 3

​Next Up: Solving Exponential Equations by Rewriting

Reorder

Solve the equation with the correct steps

$$3e^{x-6}=15$$

• Divide by 3

  $$e^{x-6}=5$$

• Rewrite as a logarithm $$\ln\left(5\right)=x-6$$

• Evaluate in calculator $$1.609=x-6$$

• Add 6 $$x=7.609$$

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

Solve for x:
4^2x + 1 = 17

• x = 1
• x = -1
• x = 2
• x = -2

Multiple Choice

The price of a purse, c, can be described by the equation $$c=250\left(\frac{3}{4}\right)^t$$ where t is number of years.

How long until the purse is worth $50?

• 5.6 years

• 19.19 years

• .75 years

• 250 years

​Next Up: Solving Logarithms by Rewriting

Multiple Choice

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e" LN_e

Multiple Choice

log(x) - 5 = -2

• 20.09

• 105

• 1000

• 1

Multiple Choice

2log₆(2x + 3) = 6

• x = 106.5

• x = 100

• x = 16

• x = 50

Multiple Choice

Solve $$\ln\left(3x-5\right)=6$$  

• 136.143

• 129.674

• 150.578

• 146.134

Multiple Choice

$$\log_2\left(b+9\right)=2$$  

• x=11

• x=-7

• x=-5

• $$x=\frac{1000}{7}$$  

​Next Up: Solving Log = Log

Multiple Choice

log₅(4x-7)=log₅(x+5)

• 3

• 12

• 4

• 7

Multiple Choice

log₄(3x-1)=log₄(2x+3)

• 4

• 3

• 1

• 8

Multiple Choice

Solve for x. $$\log_3\left(2x-6\right)=\log_3\left(3x-7\right)$$  

• -3

• 14

• -8

• No solution