Final Exam Review: Unit 4 (Exponential and Log Functions)

Unit 4: Exponential and Logarithmic Functions

• ​Solve application problems involving compound interest

• Condense and expand logarithmic expressions.

• Evaluate logarithms without a calculator.

• Solve log equations and check for extraneous solutions

  • All log terms (log=log)

  • Non-log term (log=#)

• Solve exponential equations with and without logarithms.

  • Match the bases

  • Isolate base and use logarithms

​Link to Notes

Multiple Choice

Evaluate the following logarithm:
$$\log_2\sqrt{2}$$  

• -¹/₂

• -1

• 1

• ¹/₂

Multiple Choice

Evaluate the following logarithm:

$$\log_{15}1$$

• 1

• 0

• -1

• ¹/₂

Multiple Choice

Evaluate the following logarithm:

$$\log_4\left(\frac{1}{64}\right)$$  

• 3

• -¹/₃

• -3

• ¹/₃

Multiple Choice

Evaluate the following logarithm:

$$\log_3\left(\frac{1}{9}\right)$$  

• -2

• -¹/₂

• -1

• ¹/₂

Multiple Choice

Evaluate the following logarithm:

$$\log_{27}3$$

• ¹/₃

• -3

• -¹/₂

• ¹/₂

Fill in the Blank

$$\log_2\left(\frac{1}{8}\right)-\log_216$$  

Fill in the Blank

Evaluate.

$$\ln e^6$$  

Fill in the Blank

Evaluate.

$$\log_3\left(3^{-2}\right)$$  

Multiple Choice

Condense

• logxyz³
• log(xy/z³)
• logx+logy+logz³
• logx³y³z³

Multiple Choice

Expand

• log₈x+log₈y+log₈z
• 5log₈x+5log₈y+5log₈z
• log₈xy+5log₈z
• log₈x+log₈y+5log₈z

Multiple Choice

log 1000 =

• 1/10

• 10

• 1/3

• 3

Multiple Choice

log ₉ 27 =

• 3

• 2/3

• 3/2

• 1/3

Multiple Choice

$$\log_4\left(-16\right)$$  

• -2

• -1/2

• 2

• no solution

Multiple Choice

• log₅(x²z²y¹⁰)
• log₅(z²y²x¹⁰)
• log(zy²x¹⁰)
• log₅(z² + y² + x¹⁰)

Multiple Choice

• log(x) + log(z) + 4log(y)
• 3log(x) − log(z) − 4log(y)
• 3log(x) + log(z) + 4log(y)
• log(x) − 4log(z) − 3log(y)

Multiple Choice

• 6log₈(xyz)
• log₈(x) - log₈(y) - 6log₈(z)
• log₈(x) + log₈(y) - log₈(z)
• log₈(x) + log₈(y) + 6log₈(z)

Multiple Choice

Condense to a single logarithm.

  $$\log_3\left(8\right)+\log_3\left(3\right)-\log_3\left(2\right)$$  

• $$\log_3\left(12\right)\$$

• $$\log_3\left(9\right)$$

• $$\log_3\left(48\right)$$

• $$\log_3\left(8\right)$$

Multiple Choice

What does the n stand for in this formula?

• Initial amount

• Final amount

• Rate

• Time

• The number of times compounded per year

Multiple Choice

What does the P stand for in this formula?

• Initial amount

• Final amount

• Rate

• Time

• The number of times compounded per year

Multiple Choice

Arthur invests $8,911 in a retirement account with a fixed annual interest rate of 7.71% compounded continuously. What will the account balance be after 20 years?

• $41,649.38

• $51,649.38

• $61,649.38

• $71,649.38

Multiple Choice

Describe the transformation of $$y=5^x$$

$$y=5^{x-1}+2$$

• Right 1, Down 2

• Left 1, Down 2

• Left 1, Up 2

• Right 1, Up 2

Multiple Choice

Solve the exponential equation by matching the bases: $$4^{3b-3}=\frac{1}{16}$$

• 7

• -1/4

• 1/2

• 1/3

Multiple Choice

Solve the exponential equation by matching the bases:

8 = 2^5x+7

• ⅘

• ¼

• -⅘

• -¼

Multiple Choice

Solve the exponential equation by matching the bases:

$$9^{8-x}=27^{x-3}$$

• x = 5

• x = -5

• x = 1/5

• x = -1/5

Multiple Choice

Solve the exponential equation by matching the bases:

$$81^{3-x}=\left(\frac{1}{3}\right)^{^{5x-6}}$$

• 6

• -6

• 9/2

• 3/2

Multiple Choice

Convert to logarithmic form:

$$64^{\frac{1}{2}}=8$$  

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

• $$\log_8\left(64\right)=2$$  

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

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

Multiple Choice

Condense to a single logarithm.

$$\log3+\log x$$  

• $$\log\left(3x\right)$$  

• $$\log\left(3^x\right)$$  

• $$\log\left(3+x\right)$$  

• $$\log_35$$  

Multiple Choice

Solve the log equation.

$$\log\left(x+6\right)=1$$

• 4

• 4.222

• -5

• -9.550

Multiple Choice

Solve the exponential equation using logarithms.

• A
• B
• C
• D

Multiple Choice

Solve the exponential equation by using logarithms.

$$9^x-1=86$$  

• 1.9395

• 4.4659

• 2.0325

• No solution

Multiple Choice

Solve the exponential equation by using logarithms.

$$3e^{2x}+1=5$$

•  x=0.131

•  x=0.187

•  x=0.151

•  x=0.144

Multiple Choice

Rewrite $$3^4=81$$ in logarithmic form.

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

Multiple Choice

Condense to a single logarithm:

$$\log_4\left(x+4\right)-\log_4\left(x-5\right)$$  

• $$\log_49$$  

• $$\log_4\left(2x-1\right)$$  

• $$\log_4\left(x^2-x-20\right)$$  

• $$\log_4\left(\frac{x+4}{x-5}\right)$$  

Multiple Choice

Solve the log equation.

$$\log_2\left(x+8\right)=\log_264$$  

• x=16

• x=24

• x=56

• x=40

Multiple Choice

Solve the log equation.

$$\log_8\left(3x+7\right)=\log_8\left(7x+4\right)$$  

• $$x=\frac{3}{4}$$  

• $$x=3$$  

• $$x=6$$  

• $$x=\frac{4}{3}$$  

Multiple Choice

Solve the log equation.

$$\log_6x+\log_69=\log_654$$  

• x=6

• x=45

• x=7

• x=36

Multiple Choice

Solve the log equation.

$$\log_9\left(3u+14\right)-\log_95=\log_92u$$  

• u=4

• u=6

• u=2

• u=1

Multiple Choice

Solve the log equation.

$$\log_710+\log_7(2x+5)=2$$

• x = 17

• x = -1/20

• x = -9/5

• x = -13/2

Multiple Choice

Solve the log equation.

$$\log_45−\log_4(x+3)=-2$$

• x = 77

• x = -31/5

• x = -43/16

• x = 55

Multiple Choice

Solve the log equation.

$$\log(7x+2)−\log3=1$$

• x = 11/7

• x = -5/21

• x = 0

• x = 4

Multiple Choice

Solve the log equation.

$$\log_2(x+2)+\log_2x=3$$

• -4, 2

• -2, 4

• 2

• 1

Multiple Choice

The natural logarithm has what base?

• 10

• 0

• e

• -e