Question 1

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$ ​

Accepted Answer

A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 1.079$ 
C)  $\ln 8 \approx 2.079$ 
D)  $\ln 8 \approx 0.079$ 
E)  $\ln 8 \approx 4.079$ 
A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 1.079$ 
C)  $\ln 8 \approx 2.079$ 
D)  $\ln 8 \approx 0.079$ 
E)  $\ln 8 \approx 4.079$

Question 2

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $- 22 + 4 e ^ { x } = 13$ ​

Accepted Answer

A)  $\ln \frac { 35 } { 4 } \approx 1.169$ 
B)  $\ln \frac { 35 } { 4 } \approx 4.169$ 
C)  $\ln \frac { 35 } { 4 } \approx 2.169$ 
D)  $\ln \frac { 35 } { 4 } \approx 0.169$ 
E)  $\ln \frac { 35 } { 4 } \approx 3.169$ 
A)  $\ln \frac { 35 } { 4 } \approx 1.169$ 
B)  $\ln \frac { 35 } { 4 } \approx 4.169$ 
C)  $\ln \frac { 35 } { 4 } \approx 2.169$ 
D)  $\ln \frac { 35 } { 4 } \approx 0.169$ 
E)  $\ln \frac { 35 } { 4 } \approx 3.169$

Question 3

$2500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places. )​ $r = 0.06$ ​

Accepted Answer

A) 13.55 yr 
B) 10.55 yr 
C) 12.55 yr 
D) 9.55 yr 
E) 11.55 yr 
A) 13.55 yr 
B) 10.55 yr 
C) 12.55 yr 
D) 9.55 yr 
E) 11.55 yr

Question 4

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $6 ^ { - 5 x } = 0.50$ ​

Accepted Answer

A)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.072$ 
B)  $\frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.517$ 
C)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.387$ 
D)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.077$ 
E)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx - 0.077$ 
A)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.072$ 
B)  $\frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.517$ 
C)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.387$ 
D)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.077$ 
E)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx - 0.077$

Question 5

Solve the equation.Round to 3 decimal places. ​
5x = 8
​

Accepted Answer

A) x = 1.415 
B) x = 2.292 
C) x = 6.724 
D) x = 2.526 
E) x = 1.292 
A) x = 1.415 
B) x = 2.292 
C) x = 6.724 
D) x = 2.526 
E) x = 1.292

Question 6

Solve for x.Approximate the result to three decimal places.​ $e ^ { x } = 4$ ​

Accepted Answer

A)  $\ln 4 \approx 1.466$ 
B)  $\ln 4 \approx 1.476$ 
C)  $\ln 4 \approx 1.436$ 
D)  $\ln 4 \approx 1.386$ 
E)  $\ln 4 \approx 1.456$ 
A)  $\ln 4 \approx 1.466$ 
B)  $\ln 4 \approx 1.476$ 
C)  $\ln 4 \approx 1.436$ 
D)  $\ln 4 \approx 1.386$ 
E)  $\ln 4 \approx 1.456$

Question 7

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $\ln x - 5 = 0$ ​

Accepted Answer

A)  $e ^ { 5 } \approx 151.413$ 
B)  $e ^ { 5 } \approx 146.413$ 
C)  $e ^ { 5 } \approx 148.413$ 
D)  $e ^ { 5 } \approx 149.413$ 
E)  $e ^ { 5 } \approx 150.413$ 
A)  $e ^ { 5 } \approx 151.413$ 
B)  $e ^ { 5 } \approx 146.413$ 
C)  $e ^ { 5 } \approx 148.413$ 
D)  $e ^ { 5 } \approx 149.413$ 
E)  $e ^ { 5 } \approx 150.413$

Question 8

Solve for x.​ $\ln x - \ln 5 = 0$ ​

Accepted Answer

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

Question 9

Simplify the expression.​ $\log _ { 5 } 5 ^ { 9 }$ ​

Accepted Answer

A) 45 
B) 5 
C) 9 
D) 81 
E) none of these 
A) 45 
B) 5 
C) 9 
D) 81 
E) none of these

Question 10

Solve for x.​ $\log x = - 4$ ​

Accepted Answer

A)  $- 4$ 
B) 0.0001 
C)  $- 0.0001$ 
D)  $4$ 
E) 1.386 
A)  $- 4$ 
B) 0.0001 
C)  $- 0.0001$ 
D)  $4$ 
E) 1.386

Question 11

Determine whether the given x-value is a solution (or an approximate solution)of the equation.​ $\begin{array} { l } 
4 ^ { 3 x - 10 } = 16 \
x = 4
\end{array}$ ​

Accepted Answer

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

Question 12

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $2 ^ { x - 5 } = 16$ ​

Accepted Answer

A) 10 
B) 11 
C) 9 
D) -9 
E) 12 
A) 10 
B) 11 
C) 9 
D) -9 
E) 12

Question 13

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $6 ^ { x } + 8 = 57$ ​

Accepted Answer

A)  $\frac { \ln 49 } { \ln 6 } \approx 2.172$ 
B)  $\frac { \ln 49 } { \ln 6 } \approx - 0.460$ 
C)  $\frac { \ln 49 } { \ln 6 } \approx 0.514$ 
D)  $\frac { \ln 49 } { \ln 6 } \approx 0.460$ 
E)  $\frac { \ln 49 } { \ln 6 } \approx - 2.172$ 
A)  $\frac { \ln 49 } { \ln 6 } \approx 2.172$ 
B)  $\frac { \ln 49 } { \ln 6 } \approx - 0.460$ 
C)  $\frac { \ln 49 } { \ln 6 } \approx 0.514$ 
D)  $\frac { \ln 49 } { \ln 6 } \approx 0.460$ 
E)  $\frac { \ln 49 } { \ln 6 } \approx - 2.172$

Question 14

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$ ​

Accepted Answer

A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 2.079$ 
C)  $\ln 8 \approx 4.079$ 
D)  $\ln 8 \approx 1.079$ 
E)  $\ln 8 \approx 0.079$ 
A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 2.079$ 
C)  $\ln 8 \approx 4.079$ 
D)  $\ln 8 \approx 1.079$ 
E)  $\ln 8 \approx 0.079$

Question 15

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $2 \log _ { 3 } ( 0.5 x ) = 5$ ​

Accepted Answer

A)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 33.177$ 
B)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 30.177$ 
C)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 31.177$ 
D)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 29.177$ 
E)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 32.177$ 
A)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 33.177$ 
B)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 30.177$ 
C)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 31.177$ 
D)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 29.177$ 
E)  $2 \left( 3 ^ { 5 / 2 } \right) \approx 32.177$

Question 16

Solve for x.Approximate the result to three decimal places.​ $\ln x = - 2$ ​

Accepted Answer

A)  $e ^ { - 2 } \approx 7.389$ 
B)  $e ^ { - 2 } \approx 0.368$ 
C)  $e ^ { - 2 } \approx 2.718$ 
D)  $e ^ { - 2 } \approx 0.135$ 
E)  $e ^ { - 2 } \approx 1.000$ 
A)  $e ^ { - 2 } \approx 7.389$ 
B)  $e ^ { - 2 } \approx 0.368$ 
C)  $e ^ { - 2 } \approx 2.718$ 
D)  $e ^ { - 2 } \approx 0.135$ 
E)  $e ^ { - 2 } \approx 1.000$

Question 17

Solve the equation algebraically.Round the result to three decimal places.​ $\frac { 3 + \ln x } { 8 } = 0$ ​

Accepted Answer

A)  $e ^ { - 3 } \approx 2,980.958$ 
B)  $e ^ { - 3 } \approx 0$ 
C)  $e ^ { - 3 } \approx 54.598$ 
D)  $e ^ { - 3 } \approx 0.050$ 
E)  $e ^ { - 3 } \approx 20.086$ 
A)  $e ^ { - 3 } \approx 2,980.958$ 
B)  $e ^ { - 3 } \approx 0$ 
C)  $e ^ { - 3 } \approx 54.598$ 
D)  $e ^ { - 3 } \approx 0.050$ 
E)  $e ^ { - 3 } \approx 20.086$

Question 18

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $3 ^ { 8 x } = 2400$ ​

Accepted Answer

A)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.018$ 
B)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.886$ 
C)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.089$ 
D)  $\frac { \ln 2400 } { 8 \ln 3 } \approx - 0.886$ 
E)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 1.248$ 
A)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.018$ 
B)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.886$ 
C)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.089$ 
D)  $\frac { \ln 2400 } { 8 \ln 3 } \approx - 0.886$ 
E)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 1.248$

Question 19

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )$ ​

Accepted Answer

A) 8 
B) 6 
C) -1 
D) 7 
E) 9 
A) 8 
B) 6 
C) -1 
D) 7 
E) 9

Question 20

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $e ^ { 3 x } = 75$ ​

Accepted Answer

A)  $\frac { \ln 75 } { 3 } \approx 0.439$ 
B)  $\frac { \ln 75 } { 3 } \approx 2.439$ 
C)  $\frac { \ln 75 } { 3 } \approx - 0.561$ 
D)  $\frac { \ln 75 } { 3 } \approx 3.439$ 
E)  $\frac { \ln 75 } { 3 } \approx 1.439$ 
A)  $\frac { \ln 75 } { 3 } \approx 0.439$ 
B)  $\frac { \ln 75 } { 3 } \approx 2.439$ 
C)  $\frac { \ln 75 } { 3 } \approx - 0.561$ 
D)  $\frac { \ln 75 } { 3 } \approx 3.439$ 
E)  $\frac { \ln 75 } { 3 } \approx 1.439$

Exam 21: Exponential and Logarithmic Equations

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ e2x−7ex−8=0e ^ { 2 x } - 7 e ^ { x } - 8 = 0e2x−7ex−8=0 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ −22+4ex=13- 22 + 4 e ^ { x } = 13−22+4ex=13 ​

$2500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places. )​ r=0.06r = 0.06r=0.06 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ 6−5x=0.506 ^ { - 5 x } = 0.506−5x=0.50 ​

Solve the equation.Round to 3 decimal places. ​ 5x = 8 ​

Solve for x.Approximate the result to three decimal places.​ ex=4e ^ { x } = 4ex=4 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ ln⁡x−5=0\ln x - 5 = 0lnx−5=0 ​

Solve for x.​ ln⁡x−ln⁡5=0\ln x - \ln 5 = 0lnx−ln5=0 ​

Simplify the expression.​ log⁡559\log _ { 5 } 5 ^ { 9 }log5​59 ​

Solve for x.​ log⁡x=−4\log x = - 4logx=−4 ​

Determine whether the given x-value is a solution (or an approximate solution)of the equation.​ =16 x=4 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ 2x−5=162 ^ { x - 5 } = 162x−5=16 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ 6x+8=576 ^ { x } + 8 = 576x+8=57 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ e2x−7ex−8=0e ^ { 2 x } - 7 e ^ { x } - 8 = 0e2x−7ex−8=0 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ 2log⁡3(0.5x)=52 \log _ { 3 } ( 0.5 x ) = 52log3​(0.5x)=5 ​

Solve for x.Approximate the result to three decimal places.​ ln⁡x=−2\ln x = - 2lnx=−2 ​

Solve the equation algebraically.Round the result to three decimal places.​ 3+ln⁡x8=0\frac { 3 + \ln x } { 8 } = 083+lnx​=0 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ 38x=24003 ^ { 8 x } = 240038x=2400 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ log⁡5(5x−3)=log⁡5(4x+4)\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )log5​(5x−3)=log5​(4x+4) ​

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ e3x=75e ^ { 3 x } = 75e3x=75 ​

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

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $- 22 + 4 e ^ { x } = 13$

$2500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places. ) $r = 0.06$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { - 5 x } = 0.50$

Solve the equation.Round to 3 decimal places. 5^x = 8

Solve for x.Approximate the result to three decimal places. $e ^ { x } = 4$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x - 5 = 0$

Solve for x. $\ln x - \ln 5 = 0$

Simplify the expression. $\log _ { 5 } 5 ^ { 9 }$

Solve for x. $\log x = - 4$

Determine whether the given x-value is a solution (or an approximate solution)of the equation. =16 x=4

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 ^ { x - 5 } = 16$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { x } + 8 = 57$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $2 \log _ { 3 } ( 0.5 x ) = 5$

Solve for x.Approximate the result to three decimal places. $\ln x = - 2$

Solve the equation algebraically.Round the result to three decimal places. $\frac { 3 + \ln x } { 8 } = 0$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 ^ { 8 x } = 2400$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 3 x } = 75$