Question 1

Write the logarithmic equation in exponential form.​ $\log _ { 7 } \frac { 1 } { 49 } = - 2$ ​

Accepted Answer

A)  $7 ^ { - 2 } = - \frac { 1 } { 49 }$ 
B)  $7 ^ { - 2 } = \frac { 1 } { 49 }$ 
C)  $7 ^ { - 2 } = - 49$ 
D)  $7 ^ { - 2 } = 49$ 
E)  $49 ^ { - 2 } = \frac { 1 } { 7 }$ 
A)  $7 ^ { - 2 } = - \frac { 1 } { 49 }$ 
B)  $7 ^ { - 2 } = \frac { 1 } { 49 }$ 
C)  $7 ^ { - 2 } = - 49$ 
D)  $7 ^ { - 2 } = 49$ 
E)  $49 ^ { - 2 } = \frac { 1 } { 7 }$ B

Question 2

Write the exponential equation in logarithmic form.​ $2 ^ { - 2 } = \frac { 1 } { 4 }$ ​

Accepted Answer

A)  $\log _ { 4 } \frac { 1 } { 2 } = - 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = 2$ 
C)  $\log _ { 2 } 4 = 2$ 
D)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
E)  $\log _ { 2 } 4 = - 2$ 
A)  $\log _ { 4 } \frac { 1 } { 2 } = - 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = 2$ 
C)  $\log _ { 2 } 4 = 2$ 
D)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
E)  $\log _ { 2 } 4 = - 2$ D

Question 3

Write the exponential equation $e ^ { 5 / 2 } = 12.1825 \ldots$ in logarithmic form.

Accepted Answer

A)  $2.303 \log \left( \frac { 5 } { 2 } \right) = 12.1825 \ldots$ 
B)  $\log _ { 10 } ( 12.1825 \ldots ) = \frac { 5 } { 2 }$ 
C)  $\ln \left( \frac { 5 } { 2 } \right) = 12.1825 \ldots$ 
D)  $\ln ( 12.1825 \ldots ) = \frac { 5 } { 2 }$ 
E)  $\ln ( 5 ) = \frac { 12.1825 \ldots } { 2 }$ 
A)  $2.303 \log \left( \frac { 5 } { 2 } \right) = 12.1825 \ldots$ 
B)  $\log _ { 10 } ( 12.1825 \ldots ) = \frac { 5 } { 2 }$ 
C)  $\ln \left( \frac { 5 } { 2 } \right) = 12.1825 \ldots$ 
D)  $\ln ( 12.1825 \ldots ) = \frac { 5 } { 2 }$ 
E)  $\ln ( 5 ) = \frac { 12.1825 \ldots } { 2 }$ D

Question 4

Write the logarithmic equation in exponential form.​ $\ln ( 8 ) = 2.079 \ldots$ ​

Accepted Answer

A)  $e ^ { - 2079 \cdots } = - 8$ 
B)  $e ^ { - 2079 \cdots } = 8$ 
C)  $e ^ { 2.079 \cdots } = - 8$ 
D)  $e ^ { 2.079 \ldots } = \frac { 1 } { 8 }$ 
E)  $e ^ { 2.079 \cdots } = 8$ 
A)  $e ^ { - 2079 \cdots } = - 8$ 
B)  $e ^ { - 2079 \cdots } = 8$ 
C)  $e ^ { 2.079 \cdots } = - 8$ 
D)  $e ^ { 2.079 \ldots } = \frac { 1 } { 8 }$ 
E)  $e ^ { 2.079 \cdots } = 8$

Question 5

Write the logarithmic equation in exponential form.​ $\ln ( 295 ) = 5.687 \ldots$ ​

Accepted Answer

A)  $e ^ { 5.687 \cdots } = - 295$ 
B)  $e ^ { 5.687 \ldots } = 295$ 
C)  $e ^ { - 5.687 \cdots } = - 295$ 
D)  $e ^ { 5.687 \ldots } = \frac { 1 } { 295 }$ 
E)  $e ^ { - 5.687 \cdots } = 295$ 
A)  $e ^ { 5.687 \cdots } = - 295$ 
B)  $e ^ { 5.687 \ldots } = 295$ 
C)  $e ^ { - 5.687 \cdots } = - 295$ 
D)  $e ^ { 5.687 \ldots } = \frac { 1 } { 295 }$ 
E)  $e ^ { - 5.687 \cdots } = 295$

Question 6

Evaluate the function $f ( x ) = \log _ { 5 } x$ at $x = \frac { 1 } { 25 }$ without using a calculator.

Accepted Answer

A)  $\frac { 1 } { 25 }$ 
B) -3 
C) -1 
D) 25 
E) -2 
A)  $\frac { 1 } { 25 }$ 
B) -3 
C) -1 
D) 25 
E) -2

Question 7

Evaluate the function $f ( x ) = - 0.944 \ln x$ at $x = 1.906$ .Round to 3 decimal places.(You may use your calculator. )

Accepted Answer

A) -0.587 
B) 0.609 
C) -0.609 
D) 0.683 
E) undefined 
A) -0.587 
B) 0.609 
C) -0.609 
D) 0.683 
E) undefined

Question 8

Write the exponential equation in logarithmic form.​ $28 ^ { 0 } = 1$ ​

Accepted Answer

A)  $\log _ { 28 } 1 = 28$ 
B)  $\log _ { 28 } 0 = 1$ 
C)  $\log _ { 1 } 28 = 28$ 
D)  $\log _ { 1 } 28 = 0$ 
E)  $\log _ { 28 } 1 = 0$ 
A)  $\log _ { 28 } 1 = 28$ 
B)  $\log _ { 28 } 0 = 1$ 
C)  $\log _ { 1 } 28 = 28$ 
D)  $\log _ { 1 } 28 = 0$ 
E)  $\log _ { 28 } 1 = 0$

Question 9

Identify the x-intercept of the function $f ( x ) = 4 \ln ( x - 2 )$ .

Accepted Answer

A)  $x = 2$ 
B)  $x = 4$ 
C)  $x = 0$ 
D)  $x = 3$ 
E) The function has no x-intercept. 
A)  $x = 2$ 
B)  $x = 4$ 
C)  $x = 0$ 
D)  $x = 3$ 
E) The function has no x-intercept.

Question 10

Use the One-to-One Property to solve the equation for x.​ $$\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15$$ ​

Accepted Answer

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

Question 11

Write the exponential equation in logarithmic form.​ $e ^ { 1 / 2 } = 1.649$ ​

Accepted Answer

A)  $\ln 1.649 \ldots = 2$ 
B)  $\ln 1.649 \ldots = - 2$ 
C)  $\ln 1.649 \ldots = \frac { 1 } { 2 }$ 
D)  $\ln 2 \ldots = 1.649$ 
E)  $\ln 1.649 \ldots = - \frac { 1 } { 2 }$ 
A)  $\ln 1.649 \ldots = 2$ 
B)  $\ln 1.649 \ldots = - 2$ 
C)  $\ln 1.649 \ldots = \frac { 1 } { 2 }$ 
D)  $\ln 2 \ldots = 1.649$ 
E)  $\ln 1.649 \ldots = - \frac { 1 } { 2 }$

Question 12

Write the exponential equation in logarithmic form.​ $81 ^ { 1 / 2 } = 9$ ​

Accepted Answer

A)  $\log _ { 81 } 9 = \frac { 1 } { 2 }$ 
B)  $\log _ { 81 } \frac { 1 } { 2 } = 9$ 
C)  $\log _ { 81 } 9 = 2$ 
D)  $\log _ { 81 } 9 = - \frac { 1 } { 2 }$ 
E)  $\log _ { 9 } 81 = \frac { 1 } { 2 }$ 
A)  $\log _ { 81 } 9 = \frac { 1 } { 2 }$ 
B)  $\log _ { 81 } \frac { 1 } { 2 } = 9$ 
C)  $\log _ { 81 } 9 = 2$ 
D)  $\log _ { 81 } 9 = - \frac { 1 } { 2 }$ 
E)  $\log _ { 9 } 81 = \frac { 1 } { 2 }$

Question 13

Write the exponential equation in logarithmic form.​ $e ^ { 3 x } = 4$ ​

Accepted Answer

A)  $\ln 4 = - 3 x$ 
B)  $\ln 4 = - \frac { 1 } { 3 } x$ 
C)  $\ln 4 = \frac { 1 } { 3 } x$ 
D)  $\ln 4 = 3 x$ 
E)  $\ln 3 = 4 x$ 
A)  $\ln 4 = - 3 x$ 
B)  $\ln 4 = - \frac { 1 } { 3 } x$ 
C)  $\ln 4 = \frac { 1 } { 3 } x$ 
D)  $\ln 4 = 3 x$ 
E)  $\ln 3 = 4 x$

Question 14

Find the graph of the function.​ $$y = \log _ { 2 } x$$ ​

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Evaluate the function at the indicated value of $x = 64$ .​ $f ( x ) = \log _ { 8 } x$ ​

Accepted Answer

A) 0 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) -2 
E) 2 
A) 0 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) -2 
E) 2

Question 17

Use the properties of logarithms to simplify the expression.​ $9 ^ { \log _ { 9 } 17 }$ ​

Accepted Answer

A) 17 
B) 0 
C)  $- \frac { 1 } { 17 }$ 
D) -17 
E)  $\frac { 1 } { 17 }$ 
A) 17 
B) 0 
C)  $- \frac { 1 } { 17 }$ 
D) -17 
E)  $\frac { 1 } { 17 }$

Question 18

Evaluate the function at the indicated value of $x = 1$ .​ $f ( x ) = \log _ { 8 } x$ ​

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 8 }$ 
C) -8 
D) 0 
E) 8 
A)  $\frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 8 }$ 
C) -8 
D) 0 
E) 8

Question 19

Write the logarithmic equation in exponential form.​ $\log _ { 100 } 10 = \frac { 1 } { 2 }$ ​

Accepted Answer

A)  $100 ^ { 1 / 2 } = - 10$ 
B)  $100 ^ { 1 / 2 } = 10$ 
C)  $10 ^ { 1 / 2 } = 100$ 
D)  $100 ^ { 1 / 2 } = - \frac { 1 } { 10 }$ 
E)  $100 ^ { 1 / 2 } = \frac { 1 } { 10 }$ 
A)  $100 ^ { 1 / 2 } = - 10$ 
B)  $100 ^ { 1 / 2 } = 10$ 
C)  $10 ^ { 1 / 2 } = 100$ 
D)  $100 ^ { 1 / 2 } = - \frac { 1 } { 10 }$ 
E)  $100 ^ { 1 / 2 } = \frac { 1 } { 10 }$

Question 20

Evaluate the function at the indicated value of $x = \frac { 1 } { 4 }$ .Round your result to three decimal places.​ $g ( x ) = - \ln x$ ​

Accepted Answer

A) -1.386 
B) 4 
C) 2.079 
D) -2.079 
E) 1.386 
A) -1.386 
B) 4 
C) 2.079 
D) -2.079 
E) 1.386

Exam 19: Logarithmic Functions and Their Graphs

Write the logarithmic equation in exponential form.​ log⁡7149=−2\log _ { 7 } \frac { 1 } { 49 } = - 2log7​491​=−2 ​

Write the exponential equation in logarithmic form.​ 2−2=142 ^ { - 2 } = \frac { 1 } { 4 }2−2=41​ ​

Write the exponential equation e5/2=12.1825…e ^ { 5 / 2 } = 12.1825 \ldotse5/2=12.1825… in logarithmic form.

Write the logarithmic equation in exponential form.​ ln⁡(8)=2.079…\ln ( 8 ) = 2.079 \ldotsln(8)=2.079… ​

Write the logarithmic equation in exponential form.​ ln⁡(295)=5.687…\ln ( 295 ) = 5.687 \ldotsln(295)=5.687… ​

Evaluate the function f(x)=log⁡5xf ( x ) = \log _ { 5 } xf(x)=log5​x at x=125x = \frac { 1 } { 25 }x=251​ without using a calculator.

Evaluate the function f(x)=−0.944ln⁡xf ( x ) = - 0.944 \ln xf(x)=−0.944lnx at x=1.906x = 1.906x=1.906 .Round to 3 decimal places.(You may use your calculator. )

Write the exponential equation in logarithmic form.​ 280=128 ^ { 0 } = 1280=1 ​

Identify the x-intercept of the function f(x)=4ln⁡(x−2)f ( x ) = 4 \ln ( x - 2 )f(x)=4ln(x−2) .

Use the One-to-One Property to solve the equation for x.​ log⁡7(x+5)=log⁡715\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15log7​(x+5)=log7​15 ​

Write the exponential equation in logarithmic form.​ e1/2=1.649e ^ { 1 / 2 } = 1.649e1/2=1.649 ​

Write the exponential equation in logarithmic form.​ 811/2=981 ^ { 1 / 2 } = 9811/2=9 ​

Write the exponential equation in logarithmic form.​ e3x=4e ^ { 3 x } = 4e3x=4 ​

Find the graph of the function.​ y=log⁡2xy = \log _ { 2 } xy=log2​x ​

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

Evaluate the function at the indicated value of x=64x = 64x=64 .​ f(x)=log⁡8xf ( x ) = \log _ { 8 } xf(x)=log8​x ​

Use the properties of logarithms to simplify the expression.​ 9log⁡9179 ^ { \log _ { 9 } 17 }9log9​17 ​

Evaluate the function at the indicated value of x=1x = 1x=1 .​ f(x)=log⁡8xf ( x ) = \log _ { 8 } xf(x)=log8​x ​

Write the logarithmic equation in exponential form.​ log⁡10010=12\log _ { 100 } 10 = \frac { 1 } { 2 }log100​10=21​ ​

Evaluate the function at the indicated value of x=14x = \frac { 1 } { 4 }x=41​ .Round your result to three decimal places.​ g(x)=−ln⁡xg ( x ) = - \ln xg(x)=−lnx ​

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

Write the logarithmic equation in exponential form. $\log _ { 7 } \frac { 1 } { 49 } = - 2$

Write the exponential equation in logarithmic form. $2 ^ { - 2 } = \frac { 1 } { 4 }$

Write the exponential equation $e ^ { 5 / 2 } = 12.1825 \ldots$ in logarithmic form.

Write the logarithmic equation in exponential form. $\ln ( 8 ) = 2.079 \ldots$

Write the logarithmic equation in exponential form. $\ln ( 295 ) = 5.687 \ldots$

Evaluate the function $f ( x ) = \log _ { 5 } x$ at $x = \frac { 1 } { 25 }$ without using a calculator.

Evaluate the function $f ( x ) = - 0.944 \ln x$ at $x = 1.906$ .Round to 3 decimal places.(You may use your calculator. )

Write the exponential equation in logarithmic form. $28 ^ { 0 } = 1$

Identify the x-intercept of the function $f ( x ) = 4 \ln ( x - 2 )$ .

Use the One-to-One Property to solve the equation for x. $\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15$

Write the exponential equation in logarithmic form. $e ^ { 1 / 2 } = 1.649$

Write the exponential equation in logarithmic form. $81 ^ { 1 / 2 } = 9$

Write the exponential equation in logarithmic form. $e ^ { 3 x } = 4$

Find the graph of the function. $y = \log _ { 2 } x$

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

Evaluate the function at the indicated value of $x = 64$ . $f ( x ) = \log _ { 8 } x$

Use the properties of logarithms to simplify the expression. $9 ^ { \log _ { 9 } 17 }$

Evaluate the function at the indicated value of $x = 1$ . $f ( x ) = \log _ { 8 } x$

Write the logarithmic equation in exponential form. $\log _ { 100 } 10 = \frac { 1 } { 2 }$

Evaluate the function at the indicated value of $x = \frac { 1 } { 4 }$ .Round your result to three decimal places. $g ( x ) = - \ln x$