Question 1

Write the logarithmic equation as an exponential equation.
-$\log ( 100 ) = 2$

Accepted Answer

A)  $10 ^ { 100 } = 2$ 
B)  $10 ^ { 1 / 2 } = 100$ 
C)  $10 ^ { 2 } = 100$ 
D)  $10 ^ { 20 } = 100$ 
A)  $10 ^ { 100 } = 2$ 
B)  $10 ^ { 1 / 2 } = 100$ 
C)  $10 ^ { 2 } = 100$ 
D)  $10 ^ { 20 } = 100$

Question 2

Solve the problem.
-A rumor is spread at an elementary school with 1200 students according to the model $$\mathrm { N } = 1200 \left( 1 - \mathrm { e } ^ { - 0.16 \mathrm {~d} } \right)$$ where N is the number of students who have heard the rumor and d is the number of days that have elapsed since the rumor began. How many students will have heard the rumor after 5 days?

Accepted Answer

A) 1063 students 
B) 1006 students 
C) 661 students 
D) 689 students 
A) 1063 students 
B) 1006 students 
C) 661 students 
D) 689 students

Question 3

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { 4 } \left( \frac { 16 } { x } \right)$

Accepted Answer

A)  $8 - \log _ { 4 } x$ 
B)  $- 2 \log _ { 4 } x$ 
C)  $2 - \log _ { 4 } x$ 
D)  $\frac { 2 } { x }$ 
A)  $8 - \log _ { 4 } x$ 
B)  $- 2 \log _ { 4 } x$ 
C)  $2 - \log _ { 4 } x$ 
D)  $\frac { 2 } { x }$

Question 4

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$2^{ ( 2 x - 1 )} = 15$$

Accepted Answer

A)  $\{ 1.45 \}$ 
B)  $\{ 2.46 \}$ 
C)  $\{ 4.25 \}$ 
D)  $\{ 1.73 \}$ 
A)  $\{ 1.45 \}$ 
B)  $\{ 2.46 \}$ 
C)  $\{ 4.25 \}$ 
D)  $\{ 1.73 \}$

Question 5

Solve the equation.
-$\log ( 5 + x ) - \log ( x - 4 ) = \log 4$

Accepted Answer

A)  $\{ - 7 \}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ 7 \}$ 
D)  $\varnothing$ 
A)  $\{ - 7 \}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ 7 \}$ 
D)  $\varnothing$

Question 6

Write the exponential equation as an equation involving a common logarithm or a natural logarithm.
-$$10 ^ { 2 } = 100$$

Accepted Answer

A)  $\log _ { 2 } 10 = 100$ 
B)  $\log 2 = 100$ 
C)  $\log _ { 2 } 100 = 10$ 
D)  $\log 100 = 2$ 
A)  $\log _ { 2 } 10 = 100$ 
B)  $\log 2 = 100$ 
C)  $\log _ { 2 } 100 = 10$ 
D)  $\log 100 = 2$

Question 7

Solve the equation.
-$\log _ { 2 } ( x + 4 ) = 1 + \log _ { 2 } ( x - 3 )$

Accepted Answer

A)  $\{ - 7 \}$ 
B)  $\{ - 10 \}$ 
C)  $\{ 10 \}$ 
D)  $\{ 7 \}$ 
A)  $\{ - 7 \}$ 
B)  $\{ - 10 \}$ 
C)  $\{ 10 \}$ 
D)  $\{ 7 \}$

Question 8

Write the exponential equation as an equation involving a common logarithm or a natural logarithm.
-$$12 ^ { \mathrm { X } } = 144$$

Accepted Answer

A)  $\log _ { x } 144 = 12$ 
B)  $\log _ { 12 } 144 = x$ 
C)  $\log x = 12$ 
D)  $\log _ { 144 } 12 = x$ 
A)  $\log _ { x } 144 = 12$ 
B)  $\log _ { 12 } 144 = x$ 
C)  $\log x = 12$ 
D)  $\log _ { 144 } 12 = x$

Question 9

Write the logarithmic equation as an exponential equation.
-$\log _ { 5 } 25 = 2$

Accepted Answer

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

Question 10

Solve the equation.
-$$3 ^{( 6 + 3 x )} = \frac { 1 } { 27 }$$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$ 
A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$

Question 11

Solve the problem.
-Suppose your great-great grandmother invested $700 earning 3.6% interest compounded continuously 120 years ago. How much would her investment be worth today? Round to the nearest cent.

Accepted Answer

A) $52,632.04 
B) $52,620.80 
C) $818.18 
D) $52,620.83 
A) $52,632.04 
B) $52,620.80 
C) $818.18 
D) $52,620.83

Question 12

Solve the equation.
-$\log _ { 35 } ( x - 2 ) = 1 - \log _ { 35 } x$

Accepted Answer

A)  $\{ 5 \}$ 
B)  $\{ - 7 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ - 5 \}$ 
A)  $\{ 5 \}$ 
B)  $\{ - 7 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ - 5 \}$

Question 13

Solve the equation.
-$$9^{7 x + 3} = 27$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 14 } \right\}$ 
D)  $\left\{ \frac { 3 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 14 } \right\}$ 
D)  $\left\{ \frac { 3 } { 7 } \right\}$

Question 14

Solve the equation.
-$$e ^ { x - 4 } = \left( \frac { 1 } { e ^ { 3 } } \right) ^ { x + 3 }$$

Accepted Answer

A)  $\left\{ \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 13 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 2 } \right\}$ 
A)  $\left\{ \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 13 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 2 } \right\}$

Question 15

Solve the equation.
-$$\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 3 }$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ \frac { 1 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 8 } \right\}$ 
A)  $\left\{ \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ \frac { 1 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 8 } \right\}$

Question 16

Solve the equation.
-$$3 ^{( 10 - 2 x )} = 81$$

Accepted Answer

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

Question 17

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$$\log _ { 6 } x ^ { 8 }$$

Accepted Answer

A)  $8 \log _ { 6 } x ^ { 8 }$ 
B)  $6 \log x$ 
C)  $8 \log _ { 6 } x$ 
D)  $6 \log _ { 8 } x$ 
A)  $8 \log _ { 6 } x ^ { 8 }$ 
B)  $6 \log x$ 
C)  $8 \log _ { 6 } x$ 
D)  $6 \log _ { 8 } x$

Question 18

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { d } x ^ { 5 }$

Accepted Answer

A)  $- 5 \log _ { d } x$ 
B)  $5 \log _ { d } x$ 
C)  $\operatorname { dog } 5 x$ 
D)  $- d \log 5 x$ 
A)  $- 5 \log _ { d } x$ 
B)  $5 \log _ { d } x$ 
C)  $\operatorname { dog } 5 x$ 
D)  $- d \log 5 x$

Question 19

Solve the equation.
-$$2 + \log _ { 3 } ( 2 x + 5 ) - \log _ { 3 } x = 4$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 \pm \sqrt { 46 } } { 9 } \right\}$ 
D)  $\left\{ \frac { 1 + \sqrt { 46 } } { 9 } \right\}$ 
A)  $\left\{ \frac { 5 } { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 \pm \sqrt { 46 } } { 9 } \right\}$ 
D)  $\left\{ \frac { 1 + \sqrt { 46 } } { 9 } \right\}$

Question 20

Solve the equation.
-$\log ( 2 + x ) - \log ( x - 5 ) = \log 2$

Accepted Answer

A)  $\{ - 12 \}$ 
B)  $\{ 12 \}$ 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  $\varnothing$ 
A)  $\{ - 12 \}$ 
B)  $\{ 12 \}$ 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  $\varnothing$

Write the logarithmic equation as an exponential equation. - $\log ( 100 ) = 2$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 4 } \left( \frac { 16 } { x } \right)$

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $2^{ ( 2 x - 1 )} = 15$

Solve the equation. - $\log ( 5 + x ) - \log ( x - 4 ) = \log 4$

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - $10 ^ { 2 } = 100$

Solve the equation. - $\log _ { 2 } ( x + 4 ) = 1 + \log _ { 2 } ( x - 3 )$

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - $12 ^ { \mathrm { X } } = 144$

Write the logarithmic equation as an exponential equation. - $\log _ { 5 } 25 = 2$

Solve the equation. - $3 ^{( 6 + 3 x )} = \frac { 1 } { 27 }$

Solve the problem. -Suppose your great-great grandmother invested $700 earning 3.6% interest compounded continuously 120 years ago. How much would her investment be worth today? Round to the nearest cent.

Solve the equation. - $\log _ { 35 } ( x - 2 ) = 1 - \log _ { 35 } x$

Solve the equation. - $9^{7 x + 3} = 27$

Solve the equation. - $e ^ { x - 4 } = \left( \frac { 1 } { e ^ { 3 } } \right) ^ { x + 3 }$

Solve the equation. - $\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 3 }$

Solve the equation. - $3 ^{( 10 - 2 x )} = 81$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } x ^ { 8 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { d } x ^ { 5 }$

Solve the equation. - $2 + \log _ { 3 } ( 2 x + 5 ) - \log _ { 3 } x = 4$

Solve the equation. - $\log ( 2 + x ) - \log ( x - 5 ) = \log 2$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 5: Exponential and Logarithmic Functions and Equations

Write the logarithmic equation as an exponential equation. - log⁡(100)=2\log ( 100 ) = 2log(100)=2

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡4(16x)\log _ { 4 } \left( \frac { 16 } { x } \right)log4​(x16​)

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - 2(2x−1)=152^{ ( 2 x - 1 )} = 152(2x−1)=15

Solve the equation. - log⁡(5+x)−log⁡(x−4)=log⁡4\log ( 5 + x ) - \log ( x - 4 ) = \log 4log(5+x)−log(x−4)=log4

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - 102=10010 ^ { 2 } = 100102=100

Solve the equation. - log⁡2(x+4)=1+log⁡2(x−3)\log _ { 2 } ( x + 4 ) = 1 + \log _ { 2 } ( x - 3 )log2​(x+4)=1+log2​(x−3)

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - 12X=14412 ^ { \mathrm { X } } = 14412X=144

Write the logarithmic equation as an exponential equation. - log⁡525=2\log _ { 5 } 25 = 2log5​25=2

Solve the equation. - 3(6+3x)=1273 ^{( 6 + 3 x )} = \frac { 1 } { 27 }3(6+3x)=271​