Question 1

Determine whether or not $x = \frac { 3 } { 7 }$ is a solution to $3 ^ { 3 x - 3 } = 81$ .

Accepted Answer

A) no 
B) yes 
A) no 
B) yes A

Question 2

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $\ln \sqrt { x - 8 } = 7$ ​

Accepted Answer

A)  $e ^ { 14 } + 8 \approx 1,202,611.284$ 
B)  $e ^ { 14 } + 8 \approx 1,202,614.284$ 
C)  $e ^ { 14 } + 8 \approx 1,202,612.284$ 
D)  $e ^ { 14 } + 8 \approx 1,202,610.284$ 
E)  $e ^ { 14 } + 8 \approx 1,202,613.284$ 
A)  $e ^ { 14 } + 8 \approx 1,202,611.284$ 
B)  $e ^ { 14 } + 8 \approx 1,202,614.284$ 
C)  $e ^ { 14 } + 8 \approx 1,202,612.284$ 
D)  $e ^ { 14 } + 8 \approx 1,202,610.284$ 
E)  $e ^ { 14 } + 8 \approx 1,202,613.284$ C

Question 3

Solve for x: $7 \left( 10 ^ { x - 3 } \right) = 23$ .Round to 3 decimal places.

Accepted Answer

A) 0.517 
B) no solution 
C) 3.517 
D) -1.362 
E) 1.362 
A) 0.517 
B) no solution 
C) 3.517 
D) -1.362 
E) 1.362 C

Question 4

Determine whether the given x-value is a solution (or an approximate solution)of the equation.​ $\begin{array} { l } 
4 ^ { 5 x - 5 } = 256 \
x = 2
\end{array}$ ​

Accepted Answer

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

Question 5

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $2 \left( 5 ^ { 2 - x } \right) = 12$ ​

Accepted Answer

A)  $2 - \frac { \ln 6 } { \ln 5 } \approx 3.887$ 
B)  $2 - \frac { \ln 6 } { \ln 5 } \approx 1.887$ 
C)  $2 - \frac { \ln 6 } { \ln 5 } \approx 0.887$ 
D)  $2 - \frac { \ln 6 } { \ln 5 } \approx 4.887$ 
E)  $2 - \frac { \ln 6 } { \ln 5 } \approx 2.887$ 
A)  $2 - \frac { \ln 6 } { \ln 5 } \approx 3.887$ 
B)  $2 - \frac { \ln 6 } { \ln 5 } \approx 1.887$ 
C)  $2 - \frac { \ln 6 } { \ln 5 } \approx 0.887$ 
D)  $2 - \frac { \ln 6 } { \ln 5 } \approx 4.887$ 
E)  $2 - \frac { \ln 6 } { \ln 5 } \approx 2.887$

Question 6

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $9 + 2 \ln x = 4$ ​

Accepted Answer

A)  $e ^ { - 5 / 2 } \approx 1.082$ 
B)  $e ^ { - 5 / 2 } \approx - 0.918$ 
C)  $e ^ { - 5 / 2 } \approx - 1.918$ 
D)  $e ^ { - 5 / 2 } \approx 0.082$ 
E)  $e ^ { - 5 / 2 } \approx 2.082$ 
A)  $e ^ { - 5 / 2 } \approx 1.082$ 
B)  $e ^ { - 5 / 2 } \approx - 0.918$ 
C)  $e ^ { - 5 / 2 } \approx - 1.918$ 
D)  $e ^ { - 5 / 2 } \approx 0.082$ 
E)  $e ^ { - 5 / 2 } \approx 2.082$

Question 7

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $\ln 2 x = 3$ ​

Accepted Answer

A)  $\frac { e ^ { 3 } } { 2 } \approx 8.043$ 
B)  $\frac { e ^ { 3 } } { 2 } \approx 10.043$ 
C)  $\frac { e ^ { 3 } } { 2 } \approx 12.043$ 
D)  $\frac { e ^ { 3 } } { 2 } \approx 11.043$ 
E)  $\frac { e ^ { 3 } } { 2 } \approx 13.043$ 
A)  $\frac { e ^ { 3 } } { 2 } \approx 8.043$ 
B)  $\frac { e ^ { 3 } } { 2 } \approx 10.043$ 
C)  $\frac { e ^ { 3 } } { 2 } \approx 12.043$ 
D)  $\frac { e ^ { 3 } } { 2 } \approx 11.043$ 
E)  $\frac { e ^ { 3 } } { 2 } \approx 13.043$

Question 8

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $\log x = 4$ ​

Accepted Answer

A) 1,000 
B) 1,000,000 
C) 10,000 
D) 100,000 
E) 100 
A) 1,000 
B) 1,000,000 
C) 10,000 
D) 100,000 
E) 100

Question 9

$4500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places. )​ $r = 0.0315$ ​

Accepted Answer

A) 21.00 yr 
B) 20.00 yr 
C) 34.88 yr 
D) 24.00 yr 
E) 23.00 yr 
A) 21.00 yr 
B) 20.00 yr 
C) 34.88 yr 
D) 24.00 yr 
E) 23.00 yr

Question 10

Solve the equation $\log ( 1 - x ) = \log ( 10 )$ for x using the One-to-One Property.

Accepted Answer

A) 11 
B) -9 
C) -11 
D) 0 
E) The equation has no solution. 
A) 11 
B) -9 
C) -11 
D) 0 
E) The equation has no solution.

Question 11

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $8 + 7 \ln x = 14$ ​

Accepted Answer

A)  $e ^ { 6 / 7 } \approx 3.356$ 
B)  $e ^ { 6 / 7 } \approx 1.356$ 
C)  $e ^ { 6 / 7 } \approx 4.356$ 
D)  $e ^ { 6 / 7 } \approx 2.356$ 
E)  $e ^ { 6 / 7 } \approx 0.356$ 
A)  $e ^ { 6 / 7 } \approx 3.356$ 
B)  $e ^ { 6 / 7 } \approx 1.356$ 
C)  $e ^ { 6 / 7 } \approx 4.356$ 
D)  $e ^ { 6 / 7 } \approx 2.356$ 
E)  $e ^ { 6 / 7 } \approx 0.356$

Question 12

Solve for x.Approximate the result to three decimal places.​ $\log _ { 7 } x = \frac { 1 } { 2 }$ ​

Accepted Answer

A)  $\sqrt { 7 } \approx 2.828$ 
B)  $\sqrt { 7 } = 2.646$ 
C)  $\sqrt { 7 } \approx - 2.646$ 
D)  $$\sqrt { 7 } \approx 2.646$$ 
E)  $\frac { \sqrt { 7 } } { 7 } \approx 2.646$ 
A)  $\sqrt { 7 } \approx 2.828$ 
B)  $\sqrt { 7 } = 2.646$ 
C)  $\sqrt { 7 } \approx - 2.646$ 
D)  $$\sqrt { 7 } \approx 2.646$$ 
E)  $\frac { \sqrt { 7 } } { 7 } \approx 2.646$

Question 13

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $3 e ^ { x } = 15$ ​

Accepted Answer

A)  $\ln 5 \approx - 1.609$ 
B)  $\ln 5 \approx 1.099$ 
C)  $\ln 5 \approx - 1.099$ 
D)  $\ln 5 \approx 1.609$ 
E)  $\ln 5 \approx 2.708$ 
A)  $\ln 5 \approx - 1.609$ 
B)  $\ln 5 \approx 1.099$ 
C)  $\ln 5 \approx - 1.099$ 
D)  $\ln 5 \approx 1.609$ 
E)  $\ln 5 \approx 2.708$

Question 14

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $e ^ { x } - 6 = 13$ ​

Accepted Answer

A)  $\ln 19 \approx - 2.565$ 
B)  $\ln 19 \approx 2.944$ 
C)  $\ln 19 \approx 1.792$ 
D)  $\ln 19 \approx 2.565$ 
E)  $\ln 19 \approx - 2.944$ 
A)  $\ln 19 \approx - 2.565$ 
B)  $\ln 19 \approx 2.944$ 
C)  $\ln 19 \approx 1.792$ 
D)  $\ln 19 \approx 2.565$ 
E)  $\ln 19 \approx - 2.944$

Question 15

Use the One-to-One Property to solve the following equation for x. $2 ^ { 5 x } = 128$

Accepted Answer

A)  $\frac { 128 } { 5 }$ 
B)  $- \frac { 64 } { 5 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $\frac { 5 } { 7 }$ 
E) 2 
A)  $\frac { 128 } { 5 }$ 
B)  $- \frac { 64 } { 5 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $\frac { 5 } { 7 }$ 
E) 2

Question 16

Solve for x.​ $6 ^ { x } = 36$ ​

Accepted Answer

A) 8 
B) 2 
C) -2 
D) -6 
E) 6 
A) 8 
B) 2 
C) -2 
D) -6 
E) 6

Question 17

Simplify the expression.​ $6 ^ { \log _ { 6 } 4 }$ ​

Accepted Answer

A) 4 
B) 16 
C) 24 
D) 6 
E) none of these 
A) 4 
B) 16 
C) 24 
D) 6 
E) none of these

Question 18

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $e ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }$ ​

Accepted Answer

A)  $4,2$ 
B)  $3,2$ 
C)  $- 4,2$ 
D)  $0,2$ 
E)  $0 , - 2$ 
A)  $4,2$ 
B)  $3,2$ 
C)  $- 4,2$ 
D)  $0,2$ 
E)  $0 , - 2$

Question 19

Solve for x.​ $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$ ​

Accepted Answer

A) 4 
B)  $$- 3$$ 
C) 7 
D) 3 
E)  $- 4$ 
A) 4 
B)  $$- 3$$ 
C) 7 
D) 3 
E)  $- 4$

Question 20

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $4 e ^ { x } = 33$ ​

Accepted Answer

A)  $\ln \frac { 33 } { 4 } \approx 2.110$ 
B)  $\ln \frac { 33 } { 4 } \approx - 2.110$ 
C)  $\ln \frac { 4 } { 33 } \approx 2.110$ 
D)  $\ln \frac { 33 } { 4 } \approx 3.497$ 
E)  $\ln \frac { 33 } { 4 } \approx 0.114$ 
A)  $\ln \frac { 33 } { 4 } \approx 2.110$ 
B)  $\ln \frac { 33 } { 4 } \approx - 2.110$ 
C)  $\ln \frac { 4 } { 33 } \approx 2.110$ 
D)  $\ln \frac { 33 } { 4 } \approx 3.497$ 
E)  $\ln \frac { 33 } { 4 } \approx 0.114$

Exam 21: Exponential and Logarithmic Equations

Determine whether or not x=37x = \frac { 3 } { 7 }x=73​ is a solution to 33x−3=813 ^ { 3 x - 3 } = 8133x−3=81 .

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ ln⁡x−8=7\ln \sqrt { x - 8 } = 7lnx−8​=7 ​

Solve for x: 7(10x−3)=237 \left( 10 ^ { x - 3 } \right) = 237(10x−3)=23 .Round to 3 decimal places.

Determine whether the given x-value is a solution (or an approximate solution)of the equation.​ =256 x=2 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ 2(52−x)=122 \left( 5 ^ { 2 - x } \right) = 122(52−x)=12 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ 9+2ln⁡x=49 + 2 \ln x = 49+2lnx=4 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ ln⁡2x=3\ln 2 x = 3ln2x=3 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ log⁡x=4\log x = 4logx=4 ​

$4500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places. )​ r=0.0315r = 0.0315r=0.0315 ​

Solve the equation log⁡(1−x)=log⁡(10)\log ( 1 - x ) = \log ( 10 )log(1−x)=log(10) for x using the One-to-One Property.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ 8+7ln⁡x=148 + 7 \ln x = 148+7lnx=14 ​

Solve for x.Approximate the result to three decimal places.​ log⁡7x=12\log _ { 7 } x = \frac { 1 } { 2 }log7​x=21​ ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ 3ex=153 e ^ { x } = 153ex=15 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ ex−6=13e ^ { x } - 6 = 13ex−6=13 ​

Use the One-to-One Property to solve the following equation for x. 25x=1282 ^ { 5 x } = 12825x=128

Solve for x.​ 6x=366 ^ { x } = 366x=36 ​

Simplify the expression.​ 6log⁡646 ^ { \log _ { 6 } 4 }6log6​4 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ e−4x2=e3x2−14xe ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }e−4x2=e3x2−14x ​

Solve for x.​ (14)x=64\left( \frac { 1 } { 4 } \right) ^ { x } = 64(41​)x=64 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ 4ex=334 e ^ { x } = 334ex=33 ​

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

Properties of Logarithms

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

Determine whether or not $x = \frac { 3 } { 7 }$ is a solution to $3 ^ { 3 x - 3 } = 81$ .

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln \sqrt { x - 8 } = 7$

Solve for x: $7 \left( 10 ^ { x - 3 } \right) = 23$ .Round to 3 decimal places.

Determine whether the given x-value is a solution (or an approximate solution)of the equation. =256 x=2

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 5 ^ { 2 - x } \right) = 12$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $9 + 2 \ln x = 4$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln 2 x = 3$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log x = 4$

$4500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places. ) $r = 0.0315$

Solve the equation $\log ( 1 - x ) = \log ( 10 )$ for x using the One-to-One Property.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $8 + 7 \ln x = 14$

Solve for x.Approximate the result to three decimal places. $\log _ { 7 } x = \frac { 1 } { 2 }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 e ^ { x } = 15$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } - 6 = 13$

Use the One-to-One Property to solve the following equation for x. $2 ^ { 5 x } = 128$

Solve for x. $6 ^ { x } = 36$

Simplify the expression. $6 ^ { \log _ { 6 } 4 }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }$

Solve for x. $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $4 e ^ { x } = 33$