Question 1

When asked to describe logarithms in one simple sentence, the teacher said, "Logarithms are exponents". What is meant by this sentence?

Accepted Answer

Answers may vary. On

Question 2

Graph the function.
-$g(x)=\log _{2} x$

Accepted Answer

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

Question 3

Why can't $y=2^{x}$ have an $x$-intercept?

Accepted Answer

Because no

Question 4

The sales of a new product (in items per month) can be approximated by $S(x)=275+300 \log 10(3 t+1)$, where $t$ represents the number of months after the item first becomes available. Find the number of items sold per month 33 months after the item first becomes available.

Accepted Answer

A)  3275 items per month 
B)  6275 items per month 
C)  82,500 items per month 
D)  875 items per month 
A)  3275 items per month 
B)  6275 items per month 
C)  82,500 items per month 
D)  875 items per month

Question 5

Find the logarithm. Give an approximation to four decimal places
-$\log 0.00484$

Accepted Answer

A)  -2.3063 
B)  -5.3308 
C)  -2.3242 
D)  -2.3152 
A)  -2.3063 
B)  -5.3308 
C)  -2.3242 
D)  -2.3152

Question 6

If $a>1$, what two points on the graph of $f(x)=\log _{a} x$ can be found with no computation?

Accepted Answer

The answer of If $a>1$, what two points on the...

Question 7

The function $Y(x)=45.21 \ln \frac{x}{3.5}$ can be used to estimate the number of years $Y(x)$ after 1980 required for a certain country's population to reach $\mathrm{x}$ million people. In what year will the country's population reach 14 million?

Accepted Answer

A)  About 2043 
B)  About 2033 
C)  About 2053 
D)  About 2048 
A)  About 2043 
B)  About 2033 
C)  About 2053 
D)  About 2048

Question 8

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$\log _{\mathrm{b}} \mathrm{x}-\log _{\mathrm{b}} \mathrm{z}$

Accepted Answer

A)  $\log _{b} \frac{z}{x}$ 
B)  $\log _{2 b} \frac{x}{z}$ 
C)  $\log _{b} \frac{x}{z}$ 
D)  $\log _{b} x-z$ 
A)  $\log _{b} \frac{z}{x}$ 
B)  $\log _{2 b} \frac{x}{z}$ 
C)  $\log _{b} \frac{x}{z}$ 
D)  $\log _{b} x-z$

Question 9

Use the horizontal line test to determine if the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 10

Find the logarithm. Give an approximation to four decimal places
-$\ln \left(3.28 \times \mathrm{e}^{3}\right)$

Accepted Answer

A)  3.1513 
B)  -1.8122 
C)  1.1878 
D)  4.1878 
A)  3.1513 
B)  -1.8122 
C)  1.1878 
D)  4.1878

Question 11

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$\log _{x} 12-\log _{x} 6$

Accepted Answer

A)  $\log _{x} 72$ 
B)  $\log _{x} 6$ 
C)  $\log _{x} 2$ 
D)  $\frac{\log _{x} 12}{\log _{x} 6}$ 
A)  $\log _{x} 72$ 
B)  $\log _{x} 6$ 
C)  $\log _{x} 2$ 
D)  $\frac{\log _{x} 12}{\log _{x} 6}$

Question 12

Write in logarithmic form.
-$10^{-3}=0.001$

Accepted Answer

A)  $\log _{10} 0.001=-3$ 
B)  $\log _{3}-3=0.10$ 
C)  $\log _{3} 0.10=-3$ 
D)  $\log _{10}-3=0.001$ 
A)  $\log _{10} 0.001=-3$ 
B)  $\log _{3}-3=0.10$ 
C)  $\log _{3} 0.10=-3$ 
D)  $\log _{10}-3=0.001$

Question 13

Solve the equation. Give the solution to three decimal places.
-$7^{-\mathrm{x}+1}=44$

Accepted Answer

A)  $\{-0.945\}$ 
B)  $\{1.945\}$ 
C)  $\{6.364\}$ 
D)  $\{-2.945\}$ 
A)  $\{-0.945\}$ 
B)  $\{1.945\}$ 
C)  $\{6.364\}$ 
D)  $\{-2.945\}$

Question 14

Solve the equation. Give the exact solution or solutions.
-$\log (4+x)-\log (x-4)=\log 5$

Accepted Answer

A)  $\{-6\}$ 
B)  $\{2.5\}$ 
C)  $\varnothing$ 
D)  $\{6\}$ 
A)  $\{-6\}$ 
B)  $\{2.5\}$ 
C)  $\varnothing$ 
D)  $\{6\}$

Question 15

Write in logarithmic form.
-$10^{5}=100,000$

Accepted Answer

A)  $\log _{5} 10=100,000$ 
B)  $\log _{10} 100,000=5$ 
C)  $\log _{5} 100,000=10$ 
D)  $\log _{10} 5=100,000$ 
A)  $\log _{5} 10=100,000$ 
B)  $\log _{10} 100,000=5$ 
C)  $\log _{5} 100,000=10$ 
D)  $\log _{10} 5=100,000$

Question 16

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.
-$f(x)=-5 x+4$

Accepted Answer

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

Question 17

Write in exponential form.
-$\log 111=0$

Accepted Answer

A)  $11^{1}=0$ 
B)  $0^{11}=1$ 
C)  $11^{0}=1$ 
D)  $1^{11}=0$ 
A)  $11^{1}=0$ 
B)  $0^{11}=1$ 
C)  $11^{0}=1$ 
D)  $1^{11}=0$

Question 18

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$, as needed.
-Find $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$if the $\mathrm{pH}=4.4$.

Accepted Answer

A)  $4.0 \times 10-4$ 
B)  $2.5 \times 10^{-4}$ 
C)  $2.5 \times 10^{-5}$ 
D)  $4.0 \times 10-5$ 
A)  $4.0 \times 10-4$ 
B)  $2.5 \times 10^{-4}$ 
C)  $2.5 \times 10^{-5}$ 
D)  $4.0 \times 10-5$

Question 19

Evaluate the logarithm.
-$\log _{10} 100$

Accepted Answer

A)  1 
B)  2 
C)  -2 
D)  0 
A)  1 
B)  2 
C)  -2 
D)  0

Question 20

Use properties of logarithms to write each expression as a sum or difference of logarithms. Assume that variables represent positive real numbers.
-$\log _{8} x y^{2}$

Accepted Answer

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

When asked to describe logarithms in one simple sentence, the teacher said, "Logarithms are exponents". What is meant by this sentence?

Graph the function. - $g(x)=\log _{2} x$ $Graph the function. - g(x)=\log _{2} x$

Why can't $y=2^{x}$ have an $x$ -intercept?

The sales of a new product (in items per month) can be approximated by $S(x)=275+300 \log 10(3 t+1)$ , where $t$ represents the number of months after the item first becomes available. Find the number of items sold per month 33 months after the item first becomes available.

Find the logarithm. Give an approximation to four decimal places - $\log 0.00484$

If $a>1$ , what two points on the graph of $f(x)=\log _{a} x$ can be found with no computation?

The function $Y(x)=45.21 \ln \frac{x}{3.5}$ can be used to estimate the number of years $Y(x)$ after 1980 required for a certain country's population to reach $\mathrm{x}$ million people. In what year will the country's population reach 14 million?

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{\mathrm{b}} \mathrm{x}-\log _{\mathrm{b}} \mathrm{z}$

Use the horizontal line test to determine if the function is one-to-one. -

Find the logarithm. Give an approximation to four decimal places - $\ln \left(3.28 \times \mathrm{e}^{3}\right)$

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{x} 12-\log _{x} 6$

Write in logarithmic form. - $10^{-3}=0.001$

Solve the equation. Give the solution to three decimal places. - $7^{-\mathrm{x}+1}=44$

Solve the equation. Give the exact solution or solutions. - $\log (4+x)-\log (x-4)=\log 5$

Write in logarithmic form. - $10^{5}=100,000$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f(x)=-5 x+4$

Write in exponential form. - $\log 111=0$

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ , as needed. -Find $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ if the $\mathrm{pH}=4.4$ .

Evaluate the logarithm. - $\log _{10} 100$

Use properties of logarithms to write each expression as a sum or difference of logarithms. Assume that variables represent positive real numbers. - $\log _{8} x y^{2}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 10: Inverse, Exponential, and Logarithmic Functions

When asked to describe logarithms in one simple sentence, the teacher said, "Logarithms are exponents". What is meant by this sentence?

Graph the function. - g(x)=log⁡2xg(x)=\log _{2} xg(x)=log2​x

Why can't y=2xy=2^{x}y=2x have an xxx -intercept?

Find the logarithm. Give an approximation to four decimal places - log⁡0.00484\log 0.00484log0.00484

If a>1a>1a>1 , what two points on the graph of f(x)=log⁡axf(x)=\log _{a} xf(x)=loga​x can be found with no computation?

The function Y(x)=45.21ln⁡x3.5Y(x)=45.21 \ln \frac{x}{3.5}Y(x)=45.21ln3.5x​ can be used to estimate the number of years Y(x)Y(x)Y(x) after 1980 required for a certain country's population to reach x\mathrm{x}x million people. In what year will the country's population reach 14 million?

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - log⁡bx−log⁡bz\log _{\mathrm{b}} \mathrm{x}-\log _{\mathrm{b}} \mathrm{z}logb​x−logb​z

Use the horizontal line test to determine if the function is one-to-one. -

Find the logarithm. Give an approximation to four decimal places - ln⁡(3.28×e3)\ln \left(3.28 \times \mathrm{e}^{3}\right)ln(3.28×e3)

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - log⁡x12−log⁡x6\log _{x} 12-\log _{x} 6logx​12−logx​6

Write in logarithmic form. - 10−3=0.00110^{-3}=0.00110−3=0.001

Solve the equation. Give the solution to three decimal places. - 7−x+1=447^{-\mathrm{x}+1}=447−x+1=44

Solve the equation. Give the exact solution or solutions. - log⁡(4+x)−log⁡(x−4)=log⁡5\log (4+x)-\log (x-4)=\log 5log(4+x)−log(x−4)=log5

Write in logarithmic form. - 105=100,00010^{5}=100,000105=100,000

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - f(x)=−5x+4f(x)=-5 x+4f(x)=−5x+4

Write in exponential form. - log⁡111=0\log 111=0log111=0

Evaluate the logarithm. - log⁡10100\log _{10} 100log10​100

Use properties of logarithms to write each expression as a sum or difference of logarithms. Assume that variables represent positive real numbers. - log⁡8xy2\log _{8} x y^{2}log8​xy2

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Graph the function. - $g(x)=\log _{2} x$ $Graph the function. - g(x)=\log _{2} x$

Why can't $y=2^{x}$ have an $x$ -intercept?

Find the logarithm. Give an approximation to four decimal places - $\log 0.00484$

If $a>1$ , what two points on the graph of $f(x)=\log _{a} x$ can be found with no computation?

The function $Y(x)=45.21 \ln \frac{x}{3.5}$ can be used to estimate the number of years $Y(x)$ after 1980 required for a certain country's population to reach $\mathrm{x}$ million people. In what year will the country's population reach 14 million?

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{\mathrm{b}} \mathrm{x}-\log _{\mathrm{b}} \mathrm{z}$

Find the logarithm. Give an approximation to four decimal places - $\ln \left(3.28 \times \mathrm{e}^{3}\right)$

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{x} 12-\log _{x} 6$

Write in logarithmic form. - $10^{-3}=0.001$

Solve the equation. Give the solution to three decimal places. - $7^{-\mathrm{x}+1}=44$

Solve the equation. Give the exact solution or solutions. - $\log (4+x)-\log (x-4)=\log 5$

Write in logarithmic form. - $10^{5}=100,000$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f(x)=-5 x+4$

Write in exponential form. - $\log 111=0$

Evaluate the logarithm. - $\log _{10} 100$

Use properties of logarithms to write each expression as a sum or difference of logarithms. Assume that variables represent positive real numbers. - $\log _{8} x y^{2}$