Question 1

Put the expressions in the appropriate order: $\frac { \ln 8 } { \ln e } , \frac { \ln 8 } { e } , \ln 8$ .

Accepted Answer

A)  $\ln 8 < \frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e }$ 
B)  $\frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e } = \ln 8$ 
C) ? $\ln 8 < \frac { \ln 8 } { e } = \frac { \ln 8 } { \ln e }$ 
D)  $\frac { \ln 8 } { \ln e } < \ln 8 < \frac { \ln 8 } { \ln e }$ 
E) The expressions are equivalent. 
A)  $\ln 8 < \frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e }$ 
B)  $\frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e } = \ln 8$ 
C) ? $\ln 8 < \frac { \ln 8 } { e } = \frac { \ln 8 } { \ln e }$ 
D)  $\frac { \ln 8 } { \ln e } < \ln 8 < \frac { \ln 8 } { \ln e }$ 
E) The expressions are equivalent. B

Question 2

Rewrite the logarithm as a ratio of common logarithms. ?
Log5 16
?

Accepted Answer

A)  $\frac { \log 16 } { \log 5 }$ 
B)  $\log \frac { 16 } { 5 }$ 
C)  $\frac { \log 5 } { \log 16 }$ 
D)  $\log \frac { 5 } { 16 }$ 
E) None of these 
A)  $\frac { \log 16 } { \log 5 }$ 
B)  $\log \frac { 16 } { 5 }$ 
C)  $\frac { \log 5 } { \log 16 }$ 
D)  $\log \frac { 5 } { 16 }$ 
E) None of these A

Question 3

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
​
Log15 1,500
​

Accepted Answer

A) 5.701 
B) 3.701 
C) 2.701 
D) 6.701 
E) 4.701 
A) 5.701 
B) 3.701 
C) 2.701 
D) 6.701 
E) 4.701 C

Question 4

Rewrite the logarithm as a ratio of common logarithms. ?
Log2.7 x
?

Accepted Answer

A)  $\frac { \log 2.7 } { \log x }$ 
B) ? $\frac { \log x } { \log 2.7 }$ 
C)  $\log \frac { x } { 2.7 }$ 
D)  $\log 2.7 x$ 
E) None of these 
A)  $\frac { \log 2.7 } { \log x }$ 
B) ? $\frac { \log x } { \log 2.7 }$ 
C)  $\log \frac { x } { 2.7 }$ 
D)  $\log 2.7 x$ 
E) None of these

Question 5

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​
Log2 (42 · 74)
​

Accepted Answer

A) 4 + 9 log2 4 
B) 9 + 4 log2 4 
C) 2 + 2 log2 7 
D) 4 + 4 log2 7 
E) 2 + 4 log2 7 
A) 4 + 9 log2 4 
B) 9 + 4 log2 4 
C) 2 + 2 log2 7 
D) 4 + 4 log2 7 
E) 2 + 4 log2 7

Question 6

Assume that x,y,and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } 5 x y$ in terms of the logarithms of x and y. ?

Accepted Answer

A)  $\log _ { c } 5 + \log _ { c } x y$ 
B)  $\log _ { c } 5 + \log _ { c } x + \log _ { c } y$ 
C)  $\log _ { c } 5 + \log _ { c } x$ 
D)  $\log _ { c } 5 + \log _ { 5 } x + \log _ { 5 } y$ 
E)  $\log _ { c } 5 + \log _ { c } y$ 
A)  $\log _ { c } 5 + \log _ { c } x y$ 
B)  $\log _ { c } 5 + \log _ { c } x + \log _ { c } y$ 
C)  $\log _ { c } 5 + \log _ { c } x$ 
D)  $\log _ { c } 5 + \log _ { 5 } x + \log _ { 5 } y$ 
E)  $\log _ { c } 5 + \log _ { c } y$

Question 7

Rewrite the logarithm log4 17 in terms of the natural logarithm.

Accepted Answer

A)  $\frac { \ln 17 } { \log _ { 4 } e }$ 
B)  $\frac { \ln 4 } { \ln 17 }$ 
C)  $\frac { \ln 17 } { \ln 4 }$ 
D) ln 17 
E) ln 4 ln 17 
A)  $\frac { \ln 17 } { \log _ { 4 } e }$ 
B)  $\frac { \ln 4 } { \ln 17 }$ 
C)  $\frac { \ln 17 } { \ln 4 }$ 
D) ln 17 
E) ln 4 ln 17

Question 8

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. )? $\log _ { 8 } \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 3 } }$ ?

Accepted Answer

A) 3log8 x + 3log8 y + 3log8 z 
B) 3log8 x + 3log8 y - 3log8 z 
C)  $\frac { 3 \log _ { 8 } x } { 3 \log _ { 8 } y \times 3 \log _ { 8 } z }$ 
D) 3log8 x - 3log8 y - 3log8 z 
E) 3log8 x - 3log8 y + 3log8 z 
A) 3log8 x + 3log8 y + 3log8 z 
B) 3log8 x + 3log8 y - 3log8 z 
C)  $\frac { 3 \log _ { 8 } x } { 3 \log _ { 8 } y \times 3 \log _ { 8 } z }$ 
D) 3log8 x - 3log8 y - 3log8 z 
E) 3log8 x - 3log8 y + 3log8 z

Question 9

Simplify the expression log5 175.

Accepted Answer

A) 35log5 2 
B) 2 log5 7 
C) 7 
D) ​2 + log5 7 
E) The expression cannot be simplified. 
A) 35log5 2 
B) 2 log5 7 
C) 7 
D) ​2 + log5 7 
E) The expression cannot be simplified.

Question 10

Condense the expression to the logarithm of a single quantity. ?
Log x - 2log y + 3log z
?

Accepted Answer

A)  $\log \frac { z ^ { 3 } } { x y ^ { 2 } }$ 
B)  $\log \frac { x } { y ^ { 2 } z ^ { 3 } }$ 
C)  $\log \frac { x y ^ { 2 } } { z ^ { 3 } }$ 
D)  $\log \frac { y ^ { 2 } } { x z ^ { 3 } }$ 
E)  $$\log \frac { x z ^ { 3 } } { y ^ { 2 } }$$ 
A)  $\log \frac { z ^ { 3 } } { x y ^ { 2 } }$ 
B)  $\log \frac { x } { y ^ { 2 } z ^ { 3 } }$ 
C)  $\log \frac { x y ^ { 2 } } { z ^ { 3 } }$ 
D)  $\log \frac { y ^ { 2 } } { x z ^ { 3 } }$ 
E)  $$\log \frac { x z ^ { 3 } } { y ^ { 2 } }$$

Question 11

Condense the expression to the logarithm of a single quantity. ?
Log x - 3log(x + 1)
?

Accepted Answer

A) 3log(x(x + 1)) 
B)  $3 \log \frac { x } { ( x + 1 ) }$ 
C)  $\log \frac { x } { ( x + 1 ) ^ { 3 } }$ 
D) log(x(x + 1)3) 
E)  $\frac { 1 } { 3 } \log \frac { x } { ( x + 1 ) }$ 
A) 3log(x(x + 1)) 
B)  $3 \log \frac { x } { ( x + 1 ) }$ 
C)  $\log \frac { x } { ( x + 1 ) ^ { 3 } }$ 
D) log(x(x + 1)3) 
E)  $\frac { 1 } { 3 } \log \frac { x } { ( x + 1 ) }$

Question 12

Use the properties of logarithms to rewrite and simplify the logarithmic expression.? $\ln \left( \frac { 2 } { e ^ { 3 } } \right)$ ?

Accepted Answer

A) ln 2 
B) ln 5 
C) ln 2 - 3 
D) ln 3 - 2 
E) ln 3 
A) ln 2 
B) ln 5 
C) ln 2 - 3 
D) ln 3 - 2 
E) ln 3

Question 13

Assume that x,y,z and b are positive numbers.Use the properties of logarithms to write the expression $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$ in terms of the logarithms of x,y,and z. ?

Accepted Answer

A)  $\frac { 5 } { 4 } \log _ { b } x + \log _ { b } y - \log _ { b } z$ 
B)  $\frac { 5 } { 4 } \log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
C)  $\log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
D)  $\frac { 5 } { 4 } \log _ { b } ( x + y + z )$ 
E)  $20 \log _ { b } x + 8 \log _ { b } y - 16 \log _ { b } z$ 
A)  $\frac { 5 } { 4 } \log _ { b } x + \log _ { b } y - \log _ { b } z$ 
B)  $\frac { 5 } { 4 } \log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
C)  $\log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
D)  $\frac { 5 } { 4 } \log _ { b } ( x + y + z )$ 
E)  $20 \log _ { b } x + 8 \log _ { b } y - 16 \log _ { b } z$

Question 14

Condense the expression 3(log x - log y)to the logarithm of a single term.

Accepted Answer

A)  $\log \frac { x ^ { 3 } } { y }$ 
B)  $\log \frac { 3 x } { 3 y }$ 
C)  $\log \frac { x } { y ^ { 3 } }$ 
D) 3(log x - log y) 
E)  $\log \left( \frac { x } { y } \right) ^ { 3 }$ 
A)  $\log \frac { x ^ { 3 } } { y }$ 
B)  $\log \frac { 3 x } { 3 y }$ 
C)  $\log \frac { x } { y ^ { 3 } }$ 
D) 3(log x - log y) 
E)  $\log \left( \frac { x } { y } \right) ^ { 3 }$

Question 15

Evaluate the logarithm log1/3 0.603 using the change of base formula.Round to 3 decimal places.

Accepted Answer

A) 2.172 
B) 0.556 
C) -0.506 
D) -0.22 
E) 0.46 
A) 2.172 
B) 0.556 
C) -0.506 
D) -0.22 
E) 0.46

Question 16

Condense the expression to the logarithm of a single quantity.? $\frac { 1 } { 2 } \left[ \log _ { 9 } ( x + 6 ) + 2 \log _ { 9 } ( x - 6 ) \right] - 12 \log _ { 9 } x$ ?

Accepted Answer

A)  $\log _ { 9 } \frac { ( x + 6 ) \sqrt { x - 6 } } { x ^ { 6 } }$ 
B)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
C)  $\log _ { 9 } \frac { x ^ { 6 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
D)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x + 6 } } { ( x - 6 ) }$ 
E)  $\log _ { 9 } \frac { ( x - 6 ) \sqrt { x + 6 } } { x ^ { 12 } }$ 
A)  $\log _ { 9 } \frac { ( x + 6 ) \sqrt { x - 6 } } { x ^ { 6 } }$ 
B)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
C)  $\log _ { 9 } \frac { x ^ { 6 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
D)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x + 6 } } { ( x - 6 ) }$ 
E)  $\log _ { 9 } \frac { ( x - 6 ) \sqrt { x + 6 } } { x ^ { 12 } }$

Question 17

Rewrite the logarithm as a ratio of natural logarithms. ?
Log3.1 x
?

Accepted Answer

A)  $\ln \frac { x } { 3.1 }$ 
B)  $\ln 3.1 x$ 
C)  $\frac { \ln 3.1 } { \ln x }$ 
D)  $\frac { \ln x } { \ln 3.1 }$ 
E) None of these 
A)  $\ln \frac { x } { 3.1 }$ 
B)  $\ln 3.1 x$ 
C)  $\frac { \ln 3.1 } { \ln x }$ 
D)  $\frac { \ln x } { \ln 3.1 }$ 
E) None of these

Question 18

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

Accepted Answer

A) ln 9 - ln x 
B)  $\frac { \ln 9 } { \ln x }$ 
C) ln 9 × ln x 
D) ln 9 + ln x 
E) None of these 
A) ln 9 - ln x 
B)  $\frac { \ln 9 } { \ln x }$ 
C) ln 9 × ln x 
D) ln 9 + ln x 
E) None of these

Question 19

Rewrite the logarithm as a ratio of natural logarithms. ?
Log1/5 x
?

Accepted Answer

A)  $\ln \frac { x } { 5 }$ 
B)  $\frac { \ln \frac { 1 } { 5 } } { \ln x }$ 
C)  $\frac { \ln x } { \ln \frac { 1 } { 5 } }$ 
D)  $\ln 5 x$ 
E) None of these 
A)  $\ln \frac { x } { 5 }$ 
B)  $\frac { \ln \frac { 1 } { 5 } } { \ln x }$ 
C)  $\frac { \ln x } { \ln \frac { 1 } { 5 } }$ 
D)  $\ln 5 x$ 
E) None of these

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. )? $\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }$ ?

Accepted Answer

A)  $\frac { 2 } { 7 } \log x - \frac { 4 } { 7 } \log y$ 
B)  $\frac { 1 } { 14 } \log x + \frac { 1 } { 28 } \log y$ 
C)  $\frac { 7 } { 2 } \log x + \frac { 7 } { 4 } \log y$ 
D)  $14 \log x + 28 \log y$ 
E)  $\frac { 2 } { 7 } \log x + \frac { 4 } { 7 } \log y$ 
A)  $\frac { 2 } { 7 } \log x - \frac { 4 } { 7 } \log y$ 
B)  $\frac { 1 } { 14 } \log x + \frac { 1 } { 28 } \log y$ 
C)  $\frac { 7 } { 2 } \log x + \frac { 7 } { 4 } \log y$ 
D)  $14 \log x + 28 \log y$ 
E)  $\frac { 2 } { 7 } \log x + \frac { 4 } { 7 } \log y$

Exam 20: Properties of Logarithms

Put the expressions in the appropriate order: ln⁡8ln⁡e,ln⁡8e,ln⁡8\frac { \ln 8 } { \ln e } , \frac { \ln 8 } { e } , \ln 8lneln8​,eln8​,ln8 .

Rewrite the logarithm as a ratio of common logarithms. ? Log5 16 ?

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log15 1,500 ​

Rewrite the logarithm as a ratio of common logarithms. ? Log2.7 x ?

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​ Log2 (42 · 74) ​

Assume that x,y,and c are positive numbers.Use the properties of logarithms to write the expression log⁡c5xy\log _ { c } 5 x ylogc​5xy in terms of the logarithms of x and y. ?

Rewrite the logarithm log4 17 in terms of the natural logarithm.

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. )? log⁡8x3y3z3\log _ { 8 } \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 3 } }log8​y3z3x3​ ?

Simplify the expression log5 175.

Condense the expression to the logarithm of a single quantity. ? Log x - 2log y + 3log z ?

Condense the expression to the logarithm of a single quantity. ? Log x - 3log(x + 1) ?

Use the properties of logarithms to rewrite and simplify the logarithmic expression.? ln⁡(2e3)\ln \left( \frac { 2 } { e ^ { 3 } } \right)ln(e32​) ?

Assume that x,y,z and b are positive numbers.Use the properties of logarithms to write the expression log⁡bx5y2z44\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }logb​4z4x5y2​​ in terms of the logarithms of x,y,and z. ?

Condense the expression 3(log x - log y)to the logarithm of a single term.

Evaluate the logarithm log1/3 0.603 using the change of base formula.Round to 3 decimal places.

Condense the expression to the logarithm of a single quantity.? 12[log⁡9(x+6)+2log⁡9(x−6)]−12log⁡9x\frac { 1 } { 2 } \left[ \log _ { 9 } ( x + 6 ) + 2 \log _ { 9 } ( x - 6 ) \right] - 12 \log _ { 9 } x21​[log9​(x+6)+2log9​(x−6)]−12log9​x ?

Rewrite the logarithm as a ratio of natural logarithms. ? Log3.1 x ?

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

Rewrite the logarithm as a ratio of natural logarithms. ? Log1/5 x ?

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. )? log⁡x2y47\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }log7y4x2​​ ?

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

Put the expressions in the appropriate order: $\frac { \ln 8 } { \ln e } , \frac { \ln 8 } { e } , \ln 8$ .

Rewrite the logarithm as a ratio of common logarithms. ? Log₅ 16 ?

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₁₅ 1,500

Rewrite the logarithm as a ratio of common logarithms. ? Log_2.7 x ?

Use the properties of logarithms to rewrite and simplify the logarithmic expression. Log₂ (4² · 7⁴⁾

Assume that x,y,and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } 5 x y$ in terms of the logarithms of x and y. ?

Rewrite the logarithm log₄ 17 in terms of the natural logarithm.

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. )? $\log _ { 8 } \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 3 } }$ ?

Simplify the expression log₅ 175.

Use the properties of logarithms to rewrite and simplify the logarithmic expression.? $\ln \left( \frac { 2 } { e ^ { 3 } } \right)$ ?

Assume that x,y,z and b are positive numbers.Use the properties of logarithms to write the expression $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$ in terms of the logarithms of x,y,and z. ?

Evaluate the logarithm log_1/3 0.603 using the change of base formula.Round to 3 decimal places.

Condense the expression to the logarithm of a single quantity.? $\frac { 1 } { 2 } \left[ \log _ { 9 } ( x + 6 ) + 2 \log _ { 9 } ( x - 6 ) \right] - 12 \log _ { 9 } x$ ?

Rewrite the logarithm as a ratio of natural logarithms. ? Log_3.1 x ?

Rewrite the logarithm as a ratio of natural logarithms. ? Log_1/5 x ?

Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. )? $\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }$ ?