Question 1

Condense the expression log4 x + log4 3 to the logarithm of a single term.

Accepted Answer

A) log4 -3x 
B) log4 3x 
C) log4 x3 
D) log(3x)4 
E) log4 (x + 3) 
A) log4 -3x 
B) log4 3x 
C) log4 x3 
D) log(3x)4 
E) log4 (x + 3)

Question 2

Rewrite the logarithm as a ratio of natural logarithms. ?
Log5 19
?

Accepted Answer

A)  $\ln \frac { 5 } { 19 }$ 
B)  $\ln \frac { 19 } { 5 }$ 
C)  $\frac { \ln 5 } { \ln 19 }$ 
D)  $\frac { \ln 19 } { \ln 5 }$ 
E) None of these 
A)  $\ln \frac { 5 } { 19 }$ 
B)  $\ln \frac { 19 } { 5 }$ 
C)  $\frac { \ln 5 } { \ln 19 }$ 
D)  $\frac { \ln 19 } { \ln 5 }$ 
E) None of these

Question 3

Find the exact value of the logarithmic expression without using a calculator. ​
Log6 216
​

Accepted Answer

A) 3 
B) 6 
C) 216 
D) 35 
E) None of these 
A) 3 
B) 6 
C) 216 
D) 35 
E) None of these

Question 4

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​
Ln (3e4)
​

Accepted Answer

A) ln 4 
B) ln 3 + 4 
C) ln 4 + 3 
D) ln 7 
E) ln 3 
A) ln 4 
B) ln 3 + 4 
C) ln 4 + 3 
D) ln 7 
E) ln 3

Question 5

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​
Log9 0.1
​

Accepted Answer

A) 2.952 
B) -0.048 
C) -1.048 
D) 1.952 
E) 0.952 
A) 2.952 
B) -0.048 
C) -1.048 
D) 1.952 
E) 0.952

Question 6

Rewrite the logarithm as a ratio of common logarithms.? $\log _ { x } \frac { 2 } { 11 }$ ?

Accepted Answer

A)  $\frac { \log x } { \log \frac { 2 } { 11 } }$ 
B)  $\frac { \log \frac { 2 } { 11 } } { \log x }$ 
C)  $\log \frac { 2 } { 11 } x$ 
D)  $\log \frac { 11 } { 2 x }$ 
E) None of these 
A)  $\frac { \log x } { \log \frac { 2 } { 11 } }$ 
B)  $\frac { \log \frac { 2 } { 11 } } { \log x }$ 
C)  $\log \frac { 2 } { 11 } x$ 
D)  $\log \frac { 11 } { 2 x }$ 
E) None of these

Question 7

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
​
Log2 7
​

Accepted Answer

A) 2.807 
B) 6.807 
C) 4.807 
D) 5.807 
E) 3.807 
A) 2.807 
B) 6.807 
C) 4.807 
D) 5.807 
E) 3.807

Question 8

Condense the expression to the logarithm of a single quantity.? $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$ ?

Accepted Answer

A)  $\ln \frac { ( x - 6 ) } { x ( x + 6 ) }$ 
B)  $$\ln \frac { ( x + 6 ) } { x ( x - 6 ) }$$ 
C)  $\ln \frac { x ( x - 6 ) } { ( x + 6 ) }$ 
D)  $\ln \frac { x } { ( x - 6 ) ( x + 6 ) }$ 
E)  $\ln \frac { x ( x + 6 ) } { ( x - 6 ) }$ 
A)  $\ln \frac { ( x - 6 ) } { x ( x + 6 ) }$ 
B)  $$\ln \frac { ( x + 6 ) } { x ( x - 6 ) }$$ 
C)  $\ln \frac { x ( x - 6 ) } { ( x + 6 ) }$ 
D)  $\ln \frac { x } { ( x - 6 ) ( x + 6 ) }$ 
E)  $\ln \frac { x ( x + 6 ) } { ( x - 6 ) }$

Question 9

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$ .

Accepted Answer

A) 3 
B) 0 
C) -9 
D) -81 
E) The expression cannot be simplified. 
A) 3 
B) 0 
C) -9 
D) -81 
E) The expression cannot be simplified.

Question 10

Use a graphing utility to graph the functions given by ?
Y1 = ln x - ln (x - 4)
?
And? $$y _ { 2 } = \ln \frac { x } { x - 4 }$$ ?
In the same viewing window.
?

Accepted Answer

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

Question 11

Condense the expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 3 \right] - \left[ \log _ { 4 } y \right]$ to the logarithm of a single term.

Accepted Answer

A)  $\log _ { 4 } \frac { ( 3 x ) ^ { 5 } } { y }$ 
B)  $\log _ { 4 } \frac { 3 x } { 5 y }$ 
C)  $\log _ { 4 } \sqrt [ 5 ] { \frac { 3 x } { y } }$ 
D)  $\log _ { 4 } \frac { \sqrt [ 5 ] { 3 x } } { y }$ 
E)  $\log _ { 4 } \sqrt [ 5 ] { 3 x } - \log _ { 4 } y$ 
A)  $\log _ { 4 } \frac { ( 3 x ) ^ { 5 } } { y }$ 
B)  $\log _ { 4 } \frac { 3 x } { 5 y }$ 
C)  $\log _ { 4 } \sqrt [ 5 ] { \frac { 3 x } { y } }$ 
D)  $\log _ { 4 } \frac { \sqrt [ 5 ] { 3 x } } { y }$ 
E)  $\log _ { 4 } \sqrt [ 5 ] { 3 x } - \log _ { 4 } y$

Question 12

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.? $\log _ { \frac { 1 } { 3 } } 6$ ?

Accepted Answer

A) -0.631 
B) 2.369 
C) 0.369 
D) -1.631 
E) 1.369 
A) -0.631 
B) 2.369 
C) 0.369 
D) -1.631 
E) 1.369

Question 13

Assume that x is a positive number.Use the properties of logarithms to write the expression ?
Logb (x + 8)- logb x as the logarithm of one quantity.
?

Accepted Answer

A)  $\log _ { b } \frac { x ^ { 2 } + 8 } { x }$ 
B)  $\log _ { b } \frac { x + 8 } { x }$ 
C)  $\log _ { b } \frac { x - 8 } { x }$ 
D)  $\log _ { b } \frac { x ^ { 2 } + 8 } { 8 }$ 
E) logb (x2 - 8x) 
A)  $\log _ { b } \frac { x ^ { 2 } + 8 } { x }$ 
B)  $\log _ { b } \frac { x + 8 } { x }$ 
C)  $\log _ { b } \frac { x - 8 } { x }$ 
D)  $\log _ { b } \frac { x ^ { 2 } + 8 } { 8 }$ 
E) logb (x2 - 8x)

Question 14

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.
?
F(x)= log4 x
?

Accepted Answer

A) f(x)= log x + log 4 = ln x + ln 4 ?   
B)  $$f ( x ) = \frac { \log 4 } { \log x } = \frac { \ln 4 } { \ln x }$$   
C)  $$f ( x ) = \log \frac { x } { 4 } = \ln \frac { x } { 4 }$$   
D)  $$f ( x ) = \log \frac { 4 } { x } = \ln \frac { 4 } { x }$$   
E)  $$f ( x ) = \frac { \log x } { \log 4 } = \frac { \ln x } { \ln 4 }$$   ? 
A) f(x)= log x + log 4 = ln x + ln 4 ?   
B)  $$f ( x ) = \frac { \log 4 } { \log x } = \frac { \ln 4 } { \ln x }$$   
C)  $$f ( x ) = \log \frac { x } { 4 } = \ln \frac { x } { 4 }$$   
D)  $$f ( x ) = \log \frac { 4 } { x } = \ln \frac { 4 } { x }$$   
E)  $$f ( x ) = \frac { \log x } { \log 4 } = \frac { \ln x } { \ln 4 }$$   ?

Question 15

Condense the expression $$\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]$$ to the logarithm of a single term.

Accepted Answer

A)  $\log _ { 6 } \frac { ( 7 x ) ^ { 3 } } { y }$ 
B)  $\log _ { 6 } \frac { \sqrt [ 3 ] { 7 x } } { y }$ 
C)  $\log _ { 6 } \sqrt [ 3 ] { \frac { 7 x } { y } }$ 
D)  $\log _ { 6 } \sqrt [ 3 ] { 7 x } - \log _ { 6 } y$ 
E)  $\log _ { 6 } \frac { 7 x } { 3 y }$ 
A)  $\log _ { 6 } \frac { ( 7 x ) ^ { 3 } } { y }$ 
B)  $\log _ { 6 } \frac { \sqrt [ 3 ] { 7 x } } { y }$ 
C)  $\log _ { 6 } \sqrt [ 3 ] { \frac { 7 x } { y } }$ 
D)  $\log _ { 6 } \sqrt [ 3 ] { 7 x } - \log _ { 6 } y$ 
E)  $\log _ { 6 } \frac { 7 x } { 3 y }$

Question 16

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.? $$f ( x ) = \log _ { \frac { 1 } { 5 } } x$$ ?

Accepted Answer

A)  $$f ( x ) = \frac { \log \frac { 1 } { 5 } } { \log x } = \frac { \ln \frac { 1 } { 5 } } { \ln x }$$   
B)  $$f ( x ) = \frac { \log x } { \log \frac { 1 } { 5 } } = \frac { \ln x } { \ln \frac { 1 } { 5 } }$$   
C)  $$f ( x ) = \log x + \log \frac { 1 } { 5 } = \ln x + \ln \frac { 1 } { 5 }$$   
D)  $$f ( x ) = \log \frac { \frac { 1 } { 5 } } { x } = \ln \frac { \frac { 1 } { 5 } } { x }$$   
E)  $$f ( x ) = \log \frac { x } { \frac { 1 } { 5 } } = \ln \frac { x } { \frac { 1 } { 5 } }$$   
A)  $$f ( x ) = \frac { \log \frac { 1 } { 5 } } { \log x } = \frac { \ln \frac { 1 } { 5 } } { \ln x }$$   
B)  $$f ( x ) = \frac { \log x } { \log \frac { 1 } { 5 } } = \frac { \ln x } { \ln \frac { 1 } { 5 } }$$   
C)  $$f ( x ) = \log x + \log \frac { 1 } { 5 } = \ln x + \ln \frac { 1 } { 5 }$$   
D)  $$f ( x ) = \log \frac { \frac { 1 } { 5 } } { x } = \ln \frac { \frac { 1 } { 5 } } { x }$$   
E)  $$f ( x ) = \log \frac { x } { \frac { 1 } { 5 } } = \ln \frac { x } { \frac { 1 } { 5 } }$$

Question 17

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Accepted Answer

A)  $\frac { 3 } { 49 }$ 
B)  $\frac { 14 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D) -1 
E)  $\frac { 49 } { 3 }$ 
A)  $\frac { 3 } { 49 }$ 
B)  $\frac { 14 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D) -1 
E)  $\frac { 49 } { 3 }$

Question 18

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Accepted Answer

A)  $\frac { 49 } { 3 }$ 
B)  $\frac { 3 } { 49 }$ 
C) ? $\frac { 14 } { 3 }$ 
D)  $\frac { 2 } { 3 }$ 
E) -1 
A)  $\frac { 49 } { 3 }$ 
B)  $\frac { 3 } { 49 }$ 
C) ? $\frac { 14 } { 3 }$ 
D)  $\frac { 2 } { 3 }$ 
E) -1

Question 19

Find the exact value of $\log _ { 4 } 44 - \log _ { 4 } 11$ without using a calculator.

Accepted Answer

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

Question 20

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. ) ?
Log3 9x
?

Accepted Answer

A)  $\frac { \log _ { 3 } 9 } { \log _ { 3 } x }$ 
B) log3 9? × log3 x 
C) log3 9? + log3 x 
D) log3 9? - log3 x 
E) None of these 
A)  $\frac { \log _ { 3 } 9 } { \log _ { 3 } x }$ 
B) log3 9? × log3 x 
C) log3 9? + log3 x 
D) log3 9? - log3 x 
E) None of these

Exam 20: Properties of Logarithms

Condense the expression log4 x + log4 3 to the logarithm of a single term.

Rewrite the logarithm as a ratio of natural logarithms. ? Log5 19 ?

Find the exact value of the logarithmic expression without using a calculator. ​ Log6 216 ​

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​ Ln (3e4) ​

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log9 0.1 ​

Rewrite the logarithm as a ratio of common logarithms.? log⁡x211\log _ { x } \frac { 2 } { 11 }logx​112​ ?

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log2 7 ​

Condense the expression to the logarithm of a single quantity.? ln⁡x−[ln⁡(x+6)+ln⁡(x−6)]\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]lnx−[ln(x+6)+ln(x−6)] ?

Simplify the expression log⁡3(127)3\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }log3​(271​)3 .

Use a graphing utility to graph the functions given by ? Y1 = ln x - ln (x - 4) ? And? y2=ln⁡xx−4y _ { 2 } = \ln \frac { x } { x - 4 }y2​=lnx−4x​ ? In the same viewing window. ?

Condense the expression 15[log⁡4x+log⁡43]−[log⁡4y]\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 3 \right] - \left[ \log _ { 4 } y \right]51​[log4​x+log4​3]−[log4​y] to the logarithm of a single term.

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.? log⁡136\log _ { \frac { 1 } { 3 } } 6log31​​6 ?

Assume that x is a positive number.Use the properties of logarithms to write the expression ? Logb (x + 8)- logb x as the logarithm of one quantity. ?

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio. ? F(x)= log4 x ?

Condense the expression 13[log⁡6x+log⁡67]−[log⁡6y]\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]31​[log6​x+log6​7]−[log6​y] to the logarithm of a single term.

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.? f(x)=log⁡15xf ( x ) = \log _ { \frac { 1 } { 5 } } xf(x)=log51​​x ?

Find the exact value of log⁡7493\log _ { 7 } \sqrt [ 3 ] { 49 }log7​349​ without using a calculator.

Find the exact value of log⁡7493\log _ { 7 } \sqrt [ 3 ] { 49 }log7​349​ without using a calculator.

Find the exact value of log⁡444−log⁡411\log _ { 4 } 44 - \log _ { 4 } 11log4​44−log4​11 without using a calculator.

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. ) ? Log3 9x ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Condense the expression log₄ x + log₄ 3 to the logarithm of a single term.

Rewrite the logarithm as a ratio of natural logarithms. ? Log₅ 19 ?

Find the exact value of the logarithmic expression without using a calculator. Log₆ 216

Use the properties of logarithms to rewrite and simplify the logarithmic expression. Ln (3e⁴)

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₉ 0.1

Rewrite the logarithm as a ratio of common logarithms.? $\log _ { x } \frac { 2 } { 11 }$ ?

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₂ 7

Condense the expression to the logarithm of a single quantity.? $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$ ?

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$ .

Use a graphing utility to graph the functions given by ? Y₁ = ln x - ln (x - 4) ? And? $y _ { 2 } = \ln \frac { x } { x - 4 }$ ? In the same viewing window. ?

Condense the expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 3 \right] - \left[ \log _ { 4 } y \right]$ to the logarithm of a single term.

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.? $\log _ { \frac { 1 } { 3 } } 6$ ?

Assume that x is a positive number.Use the properties of logarithms to write the expression ? Log_b (x + 8)- log_b x as the logarithm of one quantity. ?

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio. ? F(x)= log₄ x ?

Condense the expression $\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]$ to the logarithm of a single term.

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.? $f ( x ) = \log _ { \frac { 1 } { 5 } } x$ ?

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Find the exact value of $\log _ { 4 } 44 - \log _ { 4 } 11$ without using a calculator.

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. ) ? Log₃ 9x ?