Question 1

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 3 } 7 ^ { 5 }$

Accepted Answer

A)  $7 \log _ { 3 } 5$ 
B)  $5 \log _ { 3 } 7$ 
C)  $3 \log _ { 5 } 7$ 
D)  $15 \log 7$ 
A)  $7 \log _ { 3 } 5$ 
B)  $5 \log _ { 3 } 7$ 
C)  $3 \log _ { 5 } 7$ 
D)  $15 \log 7$

Question 2

Evaluate.
-$\log _ { 3 } 9$

Accepted Answer

A) 3 
B) 2 
C) 9 
D) 6 
A) 3 
B) 2 
C) 9 
D) 6

Question 3

Determine whether the given functions are inverses of each other.
-$$f ( x ) = \frac { x + 7 } { 4 } , \quad g ( x ) = 4 x + 7$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 4

Write as a logarithm of a single expression.
-$3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$

Accepted Answer

A)  $\log _ { a } 2 ( x + 1 )$ 
B)  $\log _ { a } ( 2 x + 1 ) + 2$ 
C)  $\log _ { a } ( 2 x + 3 )$ 
D)  $\log _ { a } \frac { a ^ { 2 } ( 2 x + 1 ) ^ { 3 } } { ( 2 x - 1 ) ^ { 2 } }$ 
A)  $\log _ { a } 2 ( x + 1 )$ 
B)  $\log _ { a } ( 2 x + 1 ) + 2$ 
C)  $\log _ { a } ( 2 x + 3 )$ 
D)  $\log _ { a } \frac { a ^ { 2 } ( 2 x + 1 ) ^ { 3 } } { ( 2 x - 1 ) ^ { 2 } }$

Question 5

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log ( 4 x - 1 ) = 1$$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $- \frac { 11 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 11 } { 4 }$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $- \frac { 11 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 11 } { 4 }$

Question 6

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$$f ( x ) = 6 x ^ { 2 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 1 } { 6 x ^ { 2 } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 6 } { x ^ { 2 } }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 6 \sqrt { \mathrm { x } }$ 
D) not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \frac { 1 } { 6 x ^ { 2 } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 6 } { x ^ { 2 } }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 6 \sqrt { \mathrm { x } }$ 
D) not a one-to-one function

Question 7

Write as a logarithm of a single expression.
-$$\log _ { 7 } 6 + \log _ { 7 } 4$$

Accepted Answer

A)  $\log _ { 7 } 6$ 
B)  $\log _710$ 
C)  $\log _ { 7 } 168$ 
D)  $\log _724$ 
A)  $\log _ { 7 } 6$ 
B)  $\log _710$ 
C)  $\log _ { 7 } 168$ 
D)  $\log _724$

Question 8

Solve for the indicated variable.
-$$\ln ( x - 4 ) - \ln ( y - 1 ) = \ln 3 , \quad \text { for } x$$

Accepted Answer

A) x = y + 6 
B)  $x = \frac { 4 y - 1 } { y - 1 }$ 
C)  $x = e ( y - 1 ) + 3 y + 1$ 
D)  $x = 3 y + 1$ 
A) x = y + 6 
B)  $x = \frac { 4 y - 1 } { y - 1 }$ 
C)  $x = e ( y - 1 ) + 3 y + 1$ 
D)  $x = 3 y + 1$

Question 9

For the given functions f and g , find the indicated value.
-$f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 5 x$
$( f \circ g ) ( 1 )$

Accepted Answer

A)  $\sqrt { 7 }$ 
B)  $\sqrt { 15 }$ 
C)  $5 \sqrt { 3 }$ 
D)  $5 \sqrt { 15 }$ 
A)  $\sqrt { 7 }$ 
B)  $\sqrt { 15 }$ 
C)  $5 \sqrt { 3 }$ 
D)  $5 \sqrt { 15 }$

Question 10

Find the number N. Round N to six decimal places.
-log N = -0.2918

Accepted Answer

A) 1.338835 
B) 1.957943 
C) 0.935018 
D) 0.510740 
A) 1.338835 
B) 1.957943 
C) 0.935018 
D) 0.510740

Question 11

Solve the problem.
-The value V of a car that is t years old can be modeled byed by $\mathrm { V } ( \mathrm { t } ) = 19,608 ( 0.83 ) ^ { \mathrm { t } }.$ . According to the model According to the mode, what is the value, to the nearest dollar, of a 3 year old car?

Accepted Answer

A) $4903 
B) $13,508 
C) $11,212 
D) $48,824 
A) $4903 
B) $13,508 
C) $11,212 
D) $48,824

Question 12

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { x } w ^ { z }$

Accepted Answer

A)  $z \log _ { x } w$ 
B)  $w \log _ { x } z$ 
C)  $x \log _ { w} z$ 
D)  $z \log _ { w } x$ 
A)  $z \log _ { x } w$ 
B)  $w \log _ { x } z$ 
C)  $x \log _ { w} z$ 
D)  $z \log _ { w } x$

Question 13

Write as a logarithm of a single expression.
-$5 \log _ { 4 } 3$

Accepted Answer

A) log4 15 
B) log4 1027 
C) log4 243 
D) log4 60 
A) log4 15 
B) log4 1027 
C) log4 243 
D) log4 60

Question 14

Graph the function.
-$y = \log _ { 5 } x$

Accepted Answer

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

Question 15

Determine whether the function is a one-to-one function.
-

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 16

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$$\log _83 ( x - 5 )$$

Accepted Answer

A)  $\log _ { 8 } 3 + \log _ { 8 } ( x - 5 )$ 
B)  $\log _ { 8 } 3 + \log _ { 3 } ( x - 5 )$ 
C)  $\log _83 \cdot \log _ { 3 } ( x - 5 )$ 
D)  $\log _ { 8 } 3 \cdot \log _ { 8 } ( x - 5 )$ 
A)  $\log _ { 8 } 3 + \log _ { 8 } ( x - 5 )$ 
B)  $\log _ { 8 } 3 + \log _ { 3 } ( x - 5 )$ 
C)  $\log _83 \cdot \log _ { 3 } ( x - 5 )$ 
D)  $\log _ { 8 } 3 \cdot \log _ { 8 } ( x - 5 )$

Question 17

Write the equation in exponential form.
-$\log _ { 4 } \left( \frac { 1 } { 16 } \right) = - 2$

Accepted Answer

A)  $2 ^ { 4 } = \frac { 1 } { 16 }$ 
B)  $4 ^ { 16 } = 2$ 
C)  $\left( \frac { 1 } { 16 } \right) ^ { 2 } = 4$ 
D)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
A)  $2 ^ { 4 } = \frac { 1 } { 16 }$ 
B)  $4 ^ { 16 } = 2$ 
C)  $\left( \frac { 1 } { 16 } \right) ^ { 2 } = 4$ 
D)  $4 ^ { - 2 } = \frac { 1 } { 16 }$

Question 18

Evaluate.
-$${ } _ { 10 } \log { 5 }$$

Accepted Answer

A) 100,000 
B) 5 
C) 50 
D) 0.00001 
A) 100,000 
B) 5 
C) 50 
D) 0.00001

Question 19

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.
-$f ( x ) = 4 x$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 4 }$
  
B)  $f ^ { - 1 } ( x ) = - \frac { x } { 4 }$
  
C)  $f ^ { - 1 } ( x ) = - \frac { x } { 4 }$
  
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$
  
A)  $f ^ { - 1 } ( x ) = \frac { x } { 4 }$
  
B)  $f ^ { - 1 } ( x ) = - \frac { x } { 4 }$
  
C)  $f ^ { - 1 } ( x ) = - \frac { x } { 4 }$
  
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$

Question 20

Find the antilog of the logarithm. Round the answer to six decimal places.
--2.3705

Accepted Answer

A) 10.702742 
B) 0.579362 
C) 234.692926 
D) 0.004261 
A) 10.702742 
B) 0.579362 
C) 234.692926 
D) 0.004261

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 3 } 7 ^ { 5 }$

Evaluate. - $\log _ { 3 } 9$

Determine whether the given functions are inverses of each other. - $f ( x ) = \frac { x + 7 } { 4 } , \quad g ( x ) = 4 x + 7$

Write as a logarithm of a single expression. - $3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log ( 4 x - 1 ) = 1$

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = 6 x ^ { 2 }$

Write as a logarithm of a single expression. - $\log _ { 7 } 6 + \log _ { 7 } 4$

Solve for the indicated variable. - $\ln ( x - 4 ) - \ln ( y - 1 ) = \ln 3 , \quad \text { for } x$

For the given functions f and g , find the indicated value. - $f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 5 x$ $( f \circ g ) ( 1 )$

Find the number N. Round N to six decimal places. -log N = -0.2918

Solve the problem. -The value V of a car that is t years old can be modeled byed by $\mathrm { V } ( \mathrm { t } ) = 19,608 ( 0.83 ) ^ { \mathrm { t } }.$ . According to the model According to the mode, what is the value, to the nearest dollar, of a 3 year old car?

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { x } w ^ { z }$

Write as a logarithm of a single expression. - $5 \log _ { 4 } 3$

Graph the function. - $y = \log _ { 5 } x$ $Graph the function. - y = \log _ { 5 } x$

Determine whether the function is a one-to-one function. -

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _83 ( x - 5 )$

Write the equation in exponential form. - $\log _ { 4 } \left( \frac { 1 } { 16 } \right) = - 2$

Evaluate. - ${ } _ { 10 } \log { 5 }$

Find the antilog of the logarithm. Round the answer to six decimal places. --2.3705

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 9: Exponential and Logarithmic Functions

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡375\log _ { 3 } 7 ^ { 5 }log3​75

Evaluate. - log⁡39\log _ { 3 } 9log3​9

Determine whether the given functions are inverses of each other. - f(x)=x+74,g(x)=4x+7f ( x ) = \frac { x + 7 } { 4 } , \quad g ( x ) = 4 x + 7f(x)=4x+7​,g(x)=4x+7

Write as a logarithm of a single expression. - 3log⁡a(2x+1)−2log⁡a(2x−1)+23 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 23loga​(2x+1)−2loga​(2x−1)+2

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - log⁡(4x−1)=1\log ( 4 x - 1 ) = 1log(4x−1)=1

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - f(x)=6x2f ( x ) = 6 x ^ { 2 }f(x)=6x2

Write as a logarithm of a single expression. - log⁡76+log⁡74\log _ { 7 } 6 + \log _ { 7 } 4log7​6+log7​4

Solve for the indicated variable. - ln⁡(x−4)−ln⁡(y−1)=ln⁡3, for x\ln ( x - 4 ) - \ln ( y - 1 ) = \ln 3 , \quad \text { for } xln(x−4)−ln(y−1)=ln3, for x

For the given functions f and g , find the indicated value. - f(x)=x+2,g(x)=5xf ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 5 xf(x)=x+2​,g(x)=5x (f∘g)(1)( f \circ g ) ( 1 )(f∘g)(1)