Question 1

Evaluate the function at the indicated value of $x = 0.82$ .Round your result to three decimal places.​ $f ( x ) = 9 \ln x$ ​

Accepted Answer

A) 1.786 
B) -11.674 
C) 0.82 
D) -1.786 
E) 11.674 
A) 1.786 
B) -11.674 
C) 0.82 
D) -1.786 
E) 11.674

Question 2

Write the logarithmic equation $\ln 5 = 1.609 \ldots$ in exponential form.

Accepted Answer

A)  $e ^ { 1.609 \cdots } = 5$ 
B)  $10 ^ { 5 } = 1.609 \ldots$ 
C)  $2.303 ^ { 1.609 \ldots } = 5$ 
D)  $2.303 \times 10 ^ { 5 } = 1.609 \ldots$ 
E)  $e ^ { 5 } = 1.609 \ldots$ 
A)  $e ^ { 1.609 \cdots } = 5$ 
B)  $10 ^ { 5 } = 1.609 \ldots$ 
C)  $2.303 ^ { 1.609 \ldots } = 5$ 
D)  $2.303 \times 10 ^ { 5 } = 1.609 \ldots$ 
E)  $e ^ { 5 } = 1.609 \ldots$

Question 3

Rewrite the logarithmic equation $$\log _ { 4 } \frac { 1 } { 16 } = - 2$$ in exponential form.

Accepted Answer

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

Question 4

Write the exponential equation in logarithmic form.​ $e ^ { - 0.4 } = 0.670 \ldots$ ​

Accepted Answer

A)  $\ln 0.4 = 0.670$ 
B)  $\ln 0.670 \ldots = 0.4$ 
C)  $\ln 0.670 \ldots = \frac { 1 } { 0.4 }$ 
D)  $\ln 0.670 \ldots = - \frac { 1 } { 0.4 }$ 
E)  $\ln 0.670 \ldots = - 0.4$ 
A)  $\ln 0.4 = 0.670$ 
B)  $\ln 0.670 \ldots = 0.4$ 
C)  $\ln 0.670 \ldots = \frac { 1 } { 0.4 }$ 
D)  $\ln 0.670 \ldots = - \frac { 1 } { 0.4 }$ 
E)  $\ln 0.670 \ldots = - 0.4$

Question 5

Use the One-to-One Property to solve the equation for x.​ $$\log _ { 6 } ( 8 x + 8 ) = \log _ { 6 } 4$$ ​

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B) -2 
C)  $- \frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 4 }$ 
E)  $\frac { 2 } { 3 }$ 
A)  $\frac { 3 } { 2 }$ 
B) -2 
C)  $- \frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 4 }$ 
E)  $\frac { 2 } { 3 }$

Question 6

Select the graph of the function.​ $$f ( x ) = \ln ( x + 9 )$$ ​

Accepted Answer

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

Question 7

Rewrite the exponential equation $5 ^ { - 3 } = \frac { 1 } { 125 }$ in logarithmic form.

Accepted Answer

A)  $\log _ { 5 } 125 = - 3$ 
B)  $\log _ { 125 } 5 = - 3$ 
C)  $\log _ { 3 } 125 = - 3$ 
D)  $\log _ { 5 } \frac { 1 } { 125 } = - 3$ 
E)  $\log _ { 5 } \frac { 1 } { 125 } = 3$ 
A)  $\log _ { 5 } 125 = - 3$ 
B)  $\log _ { 125 } 5 = - 3$ 
C)  $\log _ { 3 } 125 = - 3$ 
D)  $\log _ { 5 } \frac { 1 } { 125 } = - 3$ 
E)  $\log _ { 5 } \frac { 1 } { 125 } = 3$

Question 8

Use the One-to-One Property to solve the equation for x.​ $$\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6$$ ​

Accepted Answer

A) 11 
B) 14 
C) 12 
D) 13 
E) 10 
A) 11 
B) 14 
C) 12 
D) 13 
E) 10

Question 9

Write the logarithmic equation in exponential form.​ $\log _ { 32 } 2 = \frac { 1 } { 5 }$ ​

Accepted Answer

A)  $32 ^ { 1 / 5 } = - 2$ 
B)  $32 ^ { 1 / 5 } = - \frac { 1 } { 2 }$ 
C)  $2 ^ { 1 / 5 } = 32$ 
D)  $32 ^ { 1 / 5 } = 2$ 
E)  $32 ^ { 1 / 5 } = \frac { 1 } { 2 }$ 
A)  $32 ^ { 1 / 5 } = - 2$ 
B)  $32 ^ { 1 / 5 } = - \frac { 1 } { 2 }$ 
C)  $2 ^ { 1 / 5 } = 32$ 
D)  $32 ^ { 1 / 5 } = 2$ 
E)  $32 ^ { 1 / 5 } = \frac { 1 } { 2 }$

Question 10

Evaluate the function at the indicated value of $x = 3$ . ​​ $f ( x ) = \log _ { 243 } x$ ​

Accepted Answer

A)  $\frac { 1 } { 5 }$ 
B) -5 
C)  $- \frac { 1 } { 5 }$ 
D) 0 
E) 5 
A)  $\frac { 1 } { 5 }$ 
B) -5 
C)  $- \frac { 1 } { 5 }$ 
D) 0 
E) 5

Question 11

Write the logarithmic equation in exponential form.​ $\log _ { 15 } \frac { 1 } { 3375 } = - 3$ ​

Accepted Answer

A)  $3375 ^ { - 3 } = \frac { 1 } { 15 }$ 
B)  $15 ^ { - 3 } = - 3375$ 
C)  $15 ^ { - 3 } = 3375$ 
D)  $15 ^ { - 3 } = - \frac { 1 } { 3375 }$ 
E)  $15 ^ { - 3 } = \frac { 1 } { 3375 }$ 
A)  $3375 ^ { - 3 } = \frac { 1 } { 15 }$ 
B)  $15 ^ { - 3 } = - 3375$ 
C)  $15 ^ { - 3 } = 3375$ 
D)  $15 ^ { - 3 } = - \frac { 1 } { 3375 }$ 
E)  $15 ^ { - 3 } = \frac { 1 } { 3375 }$

Question 12

Write the exponential equation $e ^ { 3 / 2 } = 4.4817 \ldots$ in logarithmic form.

Accepted Answer

A)  $\ln ( 4.4817 \ldots ) = \frac { 3 } { 2 }$ 
B)  $2.303 \log \left( \frac { 3 } { 2 } \right) = 4.4817 \ldots$ 
C)  $\ln ( 4.4817 \ldots ) = \frac { 2 } { 3 }$ 
D)  $\ln \left( \frac { 3 } { 2 } \right) = 4.4817 \ldots$ 
E)  $\log _ { 10 } ( 4.4817 \ldots ) = \frac { 3 } { 2 }$ 
A)  $\ln ( 4.4817 \ldots ) = \frac { 3 } { 2 }$ 
B)  $2.303 \log \left( \frac { 3 } { 2 } \right) = 4.4817 \ldots$ 
C)  $\ln ( 4.4817 \ldots ) = \frac { 2 } { 3 }$ 
D)  $\ln \left( \frac { 3 } { 2 } \right) = 4.4817 \ldots$ 
E)  $\log _ { 10 } ( 4.4817 \ldots ) = \frac { 3 } { 2 }$

Question 13

Find the graph of the function.​ $$y = \log _ { 5 } ( x - 1 )$$ ​

Accepted Answer

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

Question 14

Solve the equation $\log ( 1 - x ) = \log ( 100 )$ for x using the One-to-One Property.

Accepted Answer

A) -101 
B) -1 
C) The equation has no solution. 
D) -99 
E) 101 
A) -101 
B) -1 
C) The equation has no solution. 
D) -99 
E) 101

Question 15

Write the logarithmic equation in exponential form.​ $$\log _ { 5 } 25 = 2$$ ​

Accepted Answer

A)  $25 ^ { 5 } = 2$ 
B)  $5 ^ { 2 } = 10$ 
C)  $5 ^ { 2 } = 55$ 
D)  $5 ^ { 2 } = 25$ 
E)  $5 ^ { 25 } = 2$ 
A)  $25 ^ { 5 } = 2$ 
B)  $5 ^ { 2 } = 10$ 
C)  $5 ^ { 2 } = 55$ 
D)  $5 ^ { 2 } = 25$ 
E)  $5 ^ { 25 } = 2$

Question 16

Use the properties of logarithms to simplify the expression.​ $\log _ { 5 } 5 ^ { 5 }$ ​

Accepted Answer

A) 0 
B) ​ $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D) -5 
E) 5 
A) 0 
B) ​ $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D) -5 
E) 5

Question 17

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.​ $x = 25.5$ ​

Accepted Answer

A) -1.407 
B) 1.407 
C) 0.711 
D) 0.039 
E) -0.711 
A) -1.407 
B) 1.407 
C) 0.711 
D) 0.039 
E) -0.711

Question 18

Evaluate the function at the indicated value of $x = 281 ^ { 5 }$ .​ $g ( x ) = \log _ { 281 } x$ ​

Accepted Answer

A) -5 
B)  $\frac { 1 } { 5 }$ 
C)  $$- \frac { 1 } { 5 }$$ 
D) 5 
E) 0 
A) -5 
B)  $\frac { 1 } { 5 }$ 
C)  $$- \frac { 1 } { 5 }$$ 
D) 5 
E) 0

Question 19

Write the exponential equation in logarithmic form.​ $e ^ { 5 } = 148.413 \ldots$ ​

Accepted Answer

A)  $\ln 148.413 \ldots = - 5$ 
B)  $\ln 148.413 \ldots = - \frac { 1 } { 5 }$ 
C)  $\ln 148.413 \ldots = 5$ 
D)  $\ln 148.413 \ldots = \frac { 1 } { 5 }$ 
E)  $\ln 5 = 148.413 \ldots$ 
A)  $\ln 148.413 \ldots = - 5$ 
B)  $\ln 148.413 \ldots = - \frac { 1 } { 5 }$ 
C)  $\ln 148.413 \ldots = 5$ 
D)  $\ln 148.413 \ldots = \frac { 1 } { 5 }$ 
E)  $\ln 5 = 148.413 \ldots$

Question 20

Write the logarithmic equation in exponential form.​ $\ln \left( \frac { 1 } { 7 } \right) = - 1.946 \ldots$ ​

Accepted Answer

A)  $e ^ { 1.946 ... } = - \frac { 1 } { 7 }$ 
B)  $e ^ { 1.946 \ldots } = \frac { 1 } { 7 }$ 
C)  $e ^ { - 1.946 \ldots } = 7$ 
D)  $e ^ { - 1.946 \ldots } = \frac { 1 } { 7 }$ 
E)  $e ^ { - 1.946 \ldots } = - \frac { 1 } { 7 }$ 
A)  $e ^ { 1.946 ... } = - \frac { 1 } { 7 }$ 
B)  $e ^ { 1.946 \ldots } = \frac { 1 } { 7 }$ 
C)  $e ^ { - 1.946 \ldots } = 7$ 
D)  $e ^ { - 1.946 \ldots } = \frac { 1 } { 7 }$ 
E)  $e ^ { - 1.946 \ldots } = - \frac { 1 } { 7 }$

Exam 19: Logarithmic Functions and Their Graphs

Evaluate the function at the indicated value of x=0.82x = 0.82x=0.82 .Round your result to three decimal places.​ f(x)=9ln⁡xf ( x ) = 9 \ln xf(x)=9lnx ​

Write the logarithmic equation ln⁡5=1.609…\ln 5 = 1.609 \ldotsln5=1.609… in exponential form.

Rewrite the logarithmic equation log⁡4116=−2\log _ { 4 } \frac { 1 } { 16 } = - 2log4​161​=−2 in exponential form.

Write the exponential equation in logarithmic form.​ e−0.4=0.670…e ^ { - 0.4 } = 0.670 \ldotse−0.4=0.670… ​

Use the One-to-One Property to solve the equation for x.​ log⁡6(8x+8)=log⁡64\log _ { 6 } ( 8 x + 8 ) = \log _ { 6 } 4log6​(8x+8)=log6​4 ​

Select the graph of the function.​ f(x)=ln⁡(x+9)f ( x ) = \ln ( x + 9 )f(x)=ln(x+9) ​

Rewrite the exponential equation 5−3=11255 ^ { - 3 } = \frac { 1 } { 125 }5−3=1251​ in logarithmic form.

Use the One-to-One Property to solve the equation for x.​ log⁡3(x−4)=log⁡36\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6log3​(x−4)=log3​6 ​

Write the logarithmic equation in exponential form.​ log⁡322=15\log _ { 32 } 2 = \frac { 1 } { 5 }log32​2=51​ ​

Evaluate the function at the indicated value of x=3x = 3x=3 . ​​ f(x)=log⁡243xf ( x ) = \log _ { 243 } xf(x)=log243​x ​

Write the logarithmic equation in exponential form.​ log⁡1513375=−3\log _ { 15 } \frac { 1 } { 3375 } = - 3log15​33751​=−3 ​

Write the exponential equation e3/2=4.4817…e ^ { 3 / 2 } = 4.4817 \ldotse3/2=4.4817… in logarithmic form.

Find the graph of the function.​ y=log⁡5(x−1)y = \log _ { 5 } ( x - 1 )y=log5​(x−1) ​

Solve the equation log⁡(1−x)=log⁡(100)\log ( 1 - x ) = \log ( 100 )log(1−x)=log(100) for x using the One-to-One Property.

Write the logarithmic equation in exponential form.​ log⁡525=2\log _ { 5 } 25 = 2log5​25=2 ​

Use the properties of logarithms to simplify the expression.​ log⁡555\log _ { 5 } 5 ^ { 5 }log5​55 ​

Evaluate f(x)=log⁡xf ( x ) = \log xf(x)=logx at the indicated value of x.Round your result to three decimal places.​ x=25.5x = 25.5x=25.5 ​

Evaluate the function at the indicated value of x=2815x = 281 ^ { 5 }x=2815 .​ g(x)=log⁡281xg ( x ) = \log _ { 281 } xg(x)=log281​x ​

Write the exponential equation in logarithmic form.​ e5=148.413…e ^ { 5 } = 148.413 \ldotse5=148.413… ​

Write the logarithmic equation in exponential form.​ ln⁡(17)=−1.946…\ln \left( \frac { 1 } { 7 } \right) = - 1.946 \ldotsln(71​)=−1.946… ​

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

Properties of Logarithms

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

Evaluate the function at the indicated value of $x = 0.82$ .Round your result to three decimal places. $f ( x ) = 9 \ln x$

Write the logarithmic equation $\ln 5 = 1.609 \ldots$ in exponential form.

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Write the exponential equation in logarithmic form. $e ^ { - 0.4 } = 0.670 \ldots$

Use the One-to-One Property to solve the equation for x. $\log _ { 6 } ( 8 x + 8 ) = \log _ { 6 } 4$

Select the graph of the function. $f ( x ) = \ln ( x + 9 )$

Rewrite the exponential equation $5 ^ { - 3 } = \frac { 1 } { 125 }$ in logarithmic form.

Use the One-to-One Property to solve the equation for x. $\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6$

Write the logarithmic equation in exponential form. $\log _ { 32 } 2 = \frac { 1 } { 5 }$

Evaluate the function at the indicated value of $x = 3$ . $f ( x ) = \log _ { 243 } x$

Write the logarithmic equation in exponential form. $\log _ { 15 } \frac { 1 } { 3375 } = - 3$

Write the exponential equation $e ^ { 3 / 2 } = 4.4817 \ldots$ in logarithmic form.

Find the graph of the function. $y = \log _ { 5 } ( x - 1 )$

Solve the equation $\log ( 1 - x ) = \log ( 100 )$ for x using the One-to-One Property.

Write the logarithmic equation in exponential form. $\log _ { 5 } 25 = 2$

Use the properties of logarithms to simplify the expression. $\log _ { 5 } 5 ^ { 5 }$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = 25.5$

Evaluate the function at the indicated value of $x = 281 ^ { 5 }$ . $g ( x ) = \log _ { 281 } x$

Write the exponential equation in logarithmic form. $e ^ { 5 } = 148.413 \ldots$

Write the logarithmic equation in exponential form. $\ln \left( \frac { 1 } { 7 } \right) = - 1.946 \ldots$