Question 1

Evaluate the expression without using a calculator.
-$\log _ { 2 } 4$

Accepted Answer

A)  2 
B)  4 
C)  $\frac { 1 } { 2 }$ 
D)  1 
A)  2 
B)  4 
C)  $\frac { 1 } { 2 }$ 
D)  1

Question 2

Evaluate the expression without using a calculator.
-$\log _ { 8 } \sqrt { 8 }$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  8 
C)  $\frac { 1 } { 8 }$ 
D)  1 
A)  $\frac { 1 } { 2 }$ 
B)  8 
C)  $\frac { 1 } { 8 }$ 
D)  1

Question 3

Write the equation in its equivalent logarithmic form.
-$$5 - 2 = \frac { 1 } { 25 }$$

Accepted Answer

A)  $\log _ { 5 } \frac { 1 } { 25 } = - 2$ 
B)  $\log _ { 1 / 5 } 5 = - 2$ 
C)  $\log _ { - 2 } \frac { 1 } { 25 } = 5$ 
D)  $\log _ { 5 } - 2 = \frac { 1 } { 25 }$ 
A)  $\log _ { 5 } \frac { 1 } { 25 } = - 2$ 
B)  $\log _ { 1 / 5 } 5 = - 2$ 
C)  $\log _ { - 2 } \frac { 1 } { 25 } = 5$ 
D)  $\log _ { 5 } - 2 = \frac { 1 } { 25 }$

Question 4

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$\log _ { 10 } 4 + \log _ { 10 } 25$

Accepted Answer

A)  2 
B)  $\log _ { 10 } 100$ 
C)  $\log _ { 10 ^ { 2 } } 29$ 
D)  $2 \log _ { 10 } 10$ 
A)  2 
B)  $\log _ { 10 } 100$ 
C)  $\log _ { 10 ^ { 2 } } 29$ 
D)  $2 \log _ { 10 } 10$

Question 5

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three
decimal places.
-$$y = 2 ( 7 ) ^ { x }$$

Accepted Answer

A)  $\mathrm { y } = 2 \mathrm { e } ^ { \mathrm { x } \ln 7 } , \mathrm { y } = 2 \mathrm { e } ^ { 1.946 \mathrm { x } }$ 
B)  $y = 7 e ^ { x } \ln 2 , y = 7 e ^ { 0.693 x }$ 
C)  $\mathrm { y } = 2 \mathrm { e } ^ { 7 \mathrm { x } } , \mathrm { y } = 22.718 ^ { 1.946 \mathrm { x } }$ 
D)  $\mathrm { y } = ( \ln 2 ) \mathrm { e } ^ { \mathrm { x } \ln 7 } , \mathrm { y } = 0.693 \mathrm { e } ^ { 1.946 \mathrm { x } }$ 
A)  $\mathrm { y } = 2 \mathrm { e } ^ { \mathrm { x } \ln 7 } , \mathrm { y } = 2 \mathrm { e } ^ { 1.946 \mathrm { x } }$ 
B)  $y = 7 e ^ { x } \ln 2 , y = 7 e ^ { 0.693 x }$ 
C)  $\mathrm { y } = 2 \mathrm { e } ^ { 7 \mathrm { x } } , \mathrm { y } = 22.718 ^ { 1.946 \mathrm { x } }$ 
D)  $\mathrm { y } = ( \ln 2 ) \mathrm { e } ^ { \mathrm { x } \ln 7 } , \mathrm { y } = 0.693 \mathrm { e } ^ { 1.946 \mathrm { x } }$

Question 6

Graph the function.
-Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = \frac { 1 } { 2 } \cdot 2 ^ { x }$.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 7

Solve the problem.
-The function $\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.01155 \mathrm { x } }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. If 500 pounds of the material are placed in the vault, how much time will need to pass for only 140 pounds to remain?

Accepted Answer

A)  110 years 
B)  115 years 
C)  120 years 
D)  220 years 
A)  110 years 
B)  115 years 
C)  120 years 
D)  220 years

Question 8

Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$4 ( 3 x + 5 ) = \frac { 1 } { 256 }$$

Accepted Answer

A)  $\{ - 3 \}$ 
B)  $\left\{ \frac { 1 } { 64 } \right\}$ 
C)  $\{ 128 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ - 3 \}$ 
B)  $\left\{ \frac { 1 } { 64 } \right\}$ 
C)  $\{ 128 \}$ 
D)  $\{ 3 \}$

Evaluate the expression without using a calculator. - $\log _ { 2 } 4$

Evaluate the expression without using a calculator. - $\log _ { 8 } \sqrt { 8 }$

Write the equation in its equivalent logarithmic form. - $5 - 2 = \frac { 1 } { 25 }$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 10 } 4 + \log _ { 10 } 25$

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - $y = 2 ( 7 ) ^ { x }$

Graph the function. -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = \frac { 1 } { 2 } \cdot 2 ^ { x }$ . $Graph the function. -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = \frac { 1 } { 2 } \cdot 2 ^ { x } .$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $4 ( 3 x + 5 ) = \frac { 1 } { 256 }$

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Exam 4: Exponential and Logarithmic Functions

Evaluate the expression without using a calculator. - log⁡24\log _ { 2 } 4log2​4

Evaluate the expression without using a calculator. - log⁡88\log _ { 8 } \sqrt { 8 }log8​8​

Write the equation in its equivalent logarithmic form. - 5−2=1255 - 2 = \frac { 1 } { 25 }5−2=251​

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - log⁡104+log⁡1025\log _ { 10 } 4 + \log _ { 10 } 25log10​4+log10​25

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - y=2(7)xy = 2 ( 7 ) ^ { x }y=2(7)x

Graph the function. -Use the graph of f(x)=2xf ( x ) = 2 ^ { x }f(x)=2x to obtain the graph of g(x)=12⋅2xg ( x ) = \frac { 1 } { 2 } \cdot 2 ^ { x }g(x)=21​⋅2x .

Solve the equation by expressing each side as a power of the same base and then equating exponents. - 4(3x+5)=12564 ( 3 x + 5 ) = \frac { 1 } { 256 }4(3x+5)=2561​