3.2 Logarithmic Functions

​3.2 Logarithmic Functions

Home

Open in new tab

Copy link

Multiple Choice

Logarithms are the inverse of ___________. #9

• Trees

• Quadratics

• Square

• Exponential

Multiple Choice

Rewrite in exponential form: #1

log₉x=2

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

Multiple Choice

Rewrite log_vn = a in exponential form. #5

• v^a = n

• n^a = v

• vⁿ = a

• aⁿ = v

Multiple Choice

Convert to logarithmic form: #14

$$64^{\frac{1}{2}}=8$$  

• $$\log_8\left(64\right)=\frac{1}{2}$$  

• $$\log_8\left(64\right)=2$$  

• l $$\log_{64}\left(\frac{1}{2}\right)=8$$  

• $$\log_{64}\left(8\right)=\frac{1}{2}$$  

Multiple Choice

Write 6^x = 8 in log form. #2

• log₆ 8 = x

• log₈ 6 = x

• log₆ x = 8

• log₈ x = 6

Multiple Choice

Rewrite log₃t = 5 in exponential form. #4

• 5^t=3

• log₃5 = log₃t

• t⁵=3

• 3⁵=t

Multiple Select

Which of the following logarithmic

expressions has been evaluated

correctly? Select all that apply. #18

• $$\log_51=0$$  

• $$\log_52=25$$  

• $$\log_5125=3$$  

• $$\log_5\left(-1\right)=0.2$$  

• $$\log_5\left(0.04\right)=-2$$  

Home

Open in new tab

Copy link

Home

Open in new tab

Copy link

Home

Open in new tab

Copy link

Multiple Choice

Which of the equations could best describe the graph?

#21

• $$\log_2\left(x+1\right)$$  

• $$\log_2\left(x-1\right)$$  

• $$\log_2\left(x\right)+1$$  

• $$\log_2\left(x\right)-1$$  

Match

Match the following log functions to their horizontal shift (which way will the asymptote shift). #23

• $$y=\ln\left(x\right)$$  

• $$y=\ln\left(x-4\right)$$  

• $$y=\ln\left(x+5\right)$$  

No Horizontal Shift

Shift Right

Shift Left

• No Horizontal Shift

• Shift Right

• Shift Left

Multiple Choice

Identify the asymptote of the transformed graph $$y=\log_2\left(x+3\right)$$  shown in red in the graph. #22

• $$x=-3$$  

• $$x=3$$  

• $$y=3$$  

• $$y=-3$$  

Multiple Choice

Graph $$y=\ln(x+1)$$  . #33

Multiple Choice

Which of the following has a domain of all real numbers, x > 2 ? #28

• y = log₂ x

• y = log₃ (x+2)

• y = log₄ (x - 2)

• y = log₇ x - 2

Multiple Choice

What is the domain of $$y=\log_3\left(x-3\right)-2$$  ? #29

• $$\left(-\infty,\infty\right)$$  

• $$\left(-2,\infty\right)$$  

• $$\left(3,\infty\right)$$  

• $$\left(-3,\infty\right)$$  

Multiple Choice

What is the range of $$y=\log_3\left(x-3\right)-2$$  ? #30

• $$\left(-\infty,\infty\right)$$  

• $$\left(2,\infty\right)$$  

• $$\left(-2,\infty\right)$$  

• $$\left(-\infty,2\right)$$  

Multiple Choice

What is the domain of the function shown? #31

• (-∞, ∞)

• (0, ∞)

• [1, ∞)

• (1, ∞)

Multiple Choice

Log with a base "e" (log_e) is the same thing as...#43

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e" LN_e

Multiple Choice

The natural logarithm has what base? #44

• 10

• 0

• e

• -e