Question 1

The graph of a logarithmic function is given. Select the function for the graph from the options.
-

Accepted Answer

A)  $f ( x ) = \log _ { 4 } x$ 
B)  $f ( x ) = - \log _ { 4 } x$ 
C)  $f ( x ) = \log _ { 4 } ( - x )$ 
D)  $f ( x ) = 1 - \log _ { 4 } x$ 
A)  $f ( x ) = \log _ { 4 } x$ 
B)  $f ( x ) = - \log _ { 4 } x$ 
C)  $f ( x ) = \log _ { 4 } ( - x )$ 
D)  $f ( x ) = 1 - \log _ { 4 } x$ D

Question 2

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { n } x ^ { 5 }$

Accepted Answer

A)  $n \log _ { 5 } x$ 
B)  $- 5 \log _ { n } x$ 
C)  $5 \log _ { n } x$ 
D)  $- n \log _ { 5 } x$ 
A)  $n \log _ { 5 } x$ 
B)  $- 5 \log _ { n } x$ 
C)  $5 \log _ { n } x$ 
D)  $- n \log _ { 5 } x$ C

Question 3

Evaluate the expression without using a calculator.
-$7 ^ { \log _ { 7 } 11 }$

Accepted Answer

A)  7 
B)  $\log _ { 7 } 11$ 
C)  11 
D)  18 
A)  7 
B)  $\log _ { 7 } 11$ 
C)  11 
D)  18 C

Question 4

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\ln \sqrt [ 7 ] { x }$

Accepted Answer

A)  $7 \ln \sqrt { x }$ 
B)  $\frac { 1 } { 7 } \ln x$ 
C)  $7 \ln x$ 
D)  $x \ln 7$ 
A)  $7 \ln \sqrt { x }$ 
B)  $\frac { 1 } { 7 } \ln x$ 
C)  $7 \ln x$ 
D)  $x \ln 7$

Question 5

Evaluate or simplify the expression without using a calculator.
-$\ln \mathrm { e }$

Accepted Answer

A)  $- 1$ 
B)  e 
C)  1 
D)  0 
A)  $- 1$ 
B)  e 
C)  1 
D)  0

Question 6

$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Find the accumulated value of an investment of $3000 at 7% compounded continuously for 6 years.

Accepted Answer

A) $4502.19 
B) $4665.88 
C) $4260.00 
D) $4565.88 
A) $4502.19 
B) $4665.88 
C) $4260.00 
D) $4565.88

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { W } \left( \frac { 13 x } { 2 } \right)$

Accepted Answer

A)  $\log _ { w } 13 + \log _ { W } x - \log _ { w } 2$ 
B)  $\log _ { W } 13 x - \log _ { w } 2$ 
C)  $\log _ { W } 13 + \log _ { W } x + \log _ { W } 2$ 
D)  $\log _ { \mathrm { W } } 11 \mathrm { x }$ 
A)  $\log _ { w } 13 + \log _ { W } x - \log _ { w } 2$ 
B)  $\log _ { W } 13 x - \log _ { w } 2$ 
C)  $\log _ { W } 13 + \log _ { W } x + \log _ { W } 2$ 
D)  $\log _ { \mathrm { W } } 11 \mathrm { x }$

Question 8

$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Find the accumulated value of an investment of $1500 at 10% compounded quarterly for 2 years.

Accepted Answer

A) $1575.94 
B) $1815.00 
C) $1800.00 
D) $1827.60 
A) $1575.94 
B) $1815.00 
C) $1800.00 
D) $1827.60

Question 9

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 2 } \left( \frac { x ^ { 2 } } { y ^ { 7 } } \right)$

Accepted Answer

A)  $2 \log _ { 2 } x - 7 \log _ { 2 } y$ 
B)  $2 \log _ { 2 } x + 7 \log _ { 2 } y$ 
C)  $7 \log _ { 2 } y - 2 \log _ { 2 } x$ 
D)  $\frac { 2 } { 7 } \log _ { 2 } \left( \frac { \mathrm { x } } { \mathrm { y } } \right)$ 
A)  $2 \log _ { 2 } x - 7 \log _ { 2 } y$ 
B)  $2 \log _ { 2 } x + 7 \log _ { 2 } y$ 
C)  $7 \log _ { 2 } y - 2 \log _ { 2 } x$ 
D)  $\frac { 2 } { 7 } \log _ { 2 } \left( \frac { \mathrm { x } } { \mathrm { y } } \right)$

Question 10

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\ln \sqrt { \frac { x } { y } }$

Accepted Answer

A)  $\frac { 1 } { 2 } \ln x - \ln y$ 
B)  $\frac { 1 } { 2 } \ln x - \frac { 1 } { 2 } \ln y$ 
C)  $\frac { 1 } { 2 } \ln \frac { x } { y }$ 
D)  $\ln \sqrt { x } - \ln \sqrt { y }$ 
A)  $\frac { 1 } { 2 } \ln x - \ln y$ 
B)  $\frac { 1 } { 2 } \ln x - \frac { 1 } { 2 } \ln y$ 
C)  $\frac { 1 } { 2 } \ln \frac { x } { y }$ 
D)  $\ln \sqrt { x } - \ln \sqrt { y }$

Question 11

Approximate the number using a calculator. Round your answer to three decimal places.
-$e ^ { - 1.4 }$

Accepted Answer

A)  $0.247$ 
B)  $- 0.247$ 
C)  $- 3.806$ 
D)  $0.547$ 
A)  $0.247$ 
B)  $- 0.247$ 
C)  $- 3.806$ 
D)  $0.547$

Question 12

Solve the problem.
-The function $\mathrm { D } ( \mathrm { h } ) = 6 \mathrm { e } ^ { - 0.4 \mathrm {~h} }$ can be used to determine the milligrams $\mathrm { D }$ of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 9 hours?

Accepted Answer

A)  $4.02 \mathrm { mg }$ 
B)  $0.16 \mathrm { mg }$ 
C)  $219.59 \mathrm { mg }$ 
D)  $0.82 \mathrm { mg }$ 
A)  $4.02 \mathrm { mg }$ 
B)  $0.16 \mathrm { mg }$ 
C)  $219.59 \mathrm { mg }$ 
D)  $0.82 \mathrm { mg }$

Question 13

Evaluate the expression without using a calculator.
-$\ln e ^ { 14 x }$

Accepted Answer

A)  $- 14 x$ 
B)  $14 x$ 
C)  $\mathrm { e } ^ { 14 \mathrm { x } }$ 
D)  $\frac { 1 } { 14 x }$ 
A)  $- 14 x$ 
B)  $14 x$ 
C)  $\mathrm { e } ^ { 14 \mathrm { x } }$ 
D)  $\frac { 1 } { 14 x }$

Question 14

Graph the function by making a table of coordinates
-$$f ( x ) = 0.3 ^ { x }$$

Accepted Answer

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

Question 15

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-

Accepted Answer

A)  $\log _ { 11 } 3 - \log _ { 11 } y - \log _ { 11 } x$ 
B)  $\frac { 1 } { 7 } \log _ { 11 } 3 - 2 \log _ { 11 } y - \log _ { 11 } x$ 
C)  $7 \log _ { 11 } 3 - 2 \log _ { 11 } y - \log _ { 11 } 7$ 
D)  $\frac { 1 } { 7 } \log _ { 11 } 3 - 2 \log _ { 11 } y - 2 \log _ { 11 } x$ 
A)  $\log _ { 11 } 3 - \log _ { 11 } y - \log _ { 11 } x$ 
B)  $\frac { 1 } { 7 } \log _ { 11 } 3 - 2 \log _ { 11 } y - \log _ { 11 } x$ 
C)  $7 \log _ { 11 } 3 - 2 \log _ { 11 } y - \log _ { 11 } 7$ 
D)  $\frac { 1 } { 7 } \log _ { 11 } 3 - 2 \log _ { 11 } y - 2 \log _ { 11 } x$

Question 16

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { b } \left( y z ^ { 4 } \right)$

Accepted Answer

A)  $4 \log _ { b } y z$ 
B)  $\log _ { b } y + \log _ { b } 4 z$ 
C)  $4 \log _ { b } y + 4 \log _ { b } z$ 
D)  $\log _ { b } y + 4 \log _ { b } z$ 
A)  $4 \log _ { b } y z$ 
B)  $\log _ { b } y + \log _ { b } 4 z$ 
C)  $4 \log _ { b } y + 4 \log _ { b } z$ 
D)  $\log _ { b } y + 4 \log _ { b } z$

Question 17

Graph the function.
-Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = 4 ^ { x + 3 } + 2$

Accepted Answer

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

Question 18

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 5 } \left( \frac { \sqrt [ 3 ] { p } \sqrt [ 4 ] { q } } { t ^ { 2 } } \right)$

Accepted Answer

A)  $3 \log _ { 5 } p + 4 \log _ { 5 } q - 2 \log _ { 5 } t$ 
B)  $\frac { 1 } { 3 } \log _ { 5 } p + \frac { 1 } { 4 } \log _ { 5 } q - 2 \log _ { 5 } t$ 
C)  $\frac { 3 } { 5 } \log _ { 5 } p + \frac { 4 } { 5 } \log _ { 5 } q - \frac { 2 } { 5 } \log _ { 5 } t$ 
D)  $\frac { 1 } { 3 } \log _ { 5 } p \cdot \frac { 1 } { 4 } \log _ { 5 } q \div 2 \log _ { 5 } t$ 
A)  $3 \log _ { 5 } p + 4 \log _ { 5 } q - 2 \log _ { 5 } t$ 
B)  $\frac { 1 } { 3 } \log _ { 5 } p + \frac { 1 } { 4 } \log _ { 5 } q - 2 \log _ { 5 } t$ 
C)  $\frac { 3 } { 5 } \log _ { 5 } p + \frac { 4 } { 5 } \log _ { 5 } q - \frac { 2 } { 5 } \log _ { 5 } t$ 
D)  $\frac { 1 } { 3 } \log _ { 5 } p \cdot \frac { 1 } { 4 } \log _ { 5 } q \div 2 \log _ { 5 } t$

Question 19

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log \left( \frac { x } { 10 } \right)$

Accepted Answer

A)  $10 x$ 
B)  $- 10 x$ 
C)  $\log x + 1$ 
D)  $\log x - 1$ 
A)  $10 x$ 
B)  $- 10 x$ 
C)  $\log x + 1$ 
D)  $\log x - 1$

Question 20

Evaluate the expression without using a calculator.
-$\log _ { 5 } \frac { 1 } { 5 }$

Accepted Answer

A)  1 
B)  5 
C)  $- 1$ 
D)  $- 5$ 
A)  1 
B)  5 
C)  $- 1$ 
D)  $- 5$

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { n } x ^ { 5 }$

Evaluate the expression without using a calculator. - $7 ^ { \log _ { 7 } 11 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 7 ] { x }$

Evaluate or simplify the expression without using a calculator. - $\ln \mathrm { e }$

$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $3000 at 7% compounded continuously for 6 years.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { W } \left( \frac { 13 x } { 2 } \right)$

$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $1500 at 10% compounded quarterly for 2 years.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \left( \frac { x ^ { 2 } } { y ^ { 7 } } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt { \frac { x } { y } }$

Approximate the number using a calculator. Round your answer to three decimal places. - $e ^ { - 1.4 }$

Evaluate the expression without using a calculator. - $\ln e ^ { 14 x }$

Graph the function by making a table of coordinates - $f ( x ) = 0.3 ^ { x }$ $Graph the function by making a table of coordinates - f ( x ) = 0.3 ^ { x }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. -

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( y z ^ { 4 } \right)$

Graph the function. -Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = 4 ^ { x + 3 } + 2$ $Graph the function. -Use the graph of f ( x ) = 4 ^ { x } to obtain the graph of g ( x ) = 4 ^ { x + 3 } + 2$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \left( \frac { \sqrt [ 3 ] { p } \sqrt [ 4 ] { q } } { t ^ { 2 } } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \left( \frac { x } { 10 } \right)$

Evaluate the expression without using a calculator. - $\log _ { 5 } \frac { 1 } { 5 }$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Filters

Exam 4: Exponential and Logarithmic Functions

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡nx5\log _ { n } x ^ { 5 }logn​x5

Evaluate the expression without using a calculator. - 7log⁡7117 ^ { \log _ { 7 } 11 }7log7​11

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡x7\ln \sqrt [ 7 ] { x }ln7x​

Evaluate or simplify the expression without using a calculator. - ln⁡e\ln \mathrm { e }lne

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡W(13x2)\log _ { W } \left( \frac { 13 x } { 2 } \right)logW​(213x​)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡2(x2y7)\log _ { 2 } \left( \frac { x ^ { 2 } } { y ^ { 7 } } \right)log2​(y7x2​)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡xy\ln \sqrt { \frac { x } { y } }lnyx​​

Approximate the number using a calculator. Round your answer to three decimal places. - e−1.4e ^ { - 1.4 }e−1.4

Evaluate the expression without using a calculator. - ln⁡e14x\ln e ^ { 14 x }lne14x

Graph the function by making a table of coordinates - f(x)=0.3xf ( x ) = 0.3 ^ { x }f(x)=0.3x