Question 1

Find the logarithm. Give an approximation to four decimal places
-$\log 117$

Accepted Answer

A)  4.7622 
B)  2.0645 
C)  2.0682 
D)  2.0719 
A)  4.7622 
B)  2.0645 
C)  2.0682 
D)  2.0719

Question 2

Solve the equation. Give the solution to three decimal places.
-$5^{\mathrm{x}+3}=10^{\mathrm{x}-4}$

Accepted Answer

A)  $\{4.120\}$ 
B)  $\{20.253\}$ 
C)  $\{3.589\}$ 
D)  $\{16.253\}$ 
A)  $\{4.120\}$ 
B)  $\{20.253\}$ 
C)  $\{3.589\}$ 
D)  $\{16.253\}$

Question 3

A student claims that since $\log _{b} x=a$ is not defined for negative values of $x$, then a must also not be negative. What is wrong with this statement?

Accepted Answer

@#LAT-DLM& is an exponent, and if a posi

Question 4

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 .
-$\log _{\mathrm{q}} 6+\log _{\mathrm{q}} \mathrm{r}$

Accepted Answer

A)  $\log _{\mathrm{q}} \frac{6}{\mathrm{r}}$ 
B)  $\log _{q} 6 r$ 
C)  $\log _{\mathrm{q}}(6+\mathrm{r})$ 
D)  $\log _{q} 6 \cdot \log _{q} r$ 
A)  $\log _{\mathrm{q}} \frac{6}{\mathrm{r}}$ 
B)  $\log _{q} 6 r$ 
C)  $\log _{\mathrm{q}}(6+\mathrm{r})$ 
D)  $\log _{q} 6 \cdot \log _{q} r$

Question 5

Sumi Kato's savings account has a balance of $\$ 715$. After 21 years, what will the amount of interest be at $4.5 \%$ compounded annually?

Accepted Answer

A)  $\$ 1075.97$ 
B)  $\$ 1092.97$ 
C)  $\$ 1086.97$ 
D)  $\$ 1501.50$ 
A)  $\$ 1075.97$ 
B)  $\$ 1092.97$ 
C)  $\$ 1086.97$ 
D)  $\$ 1501.50$

Question 6

Why can't we call $\mathrm{y}=(-2)^{\mathrm{x}}$ an exponential function?

Accepted Answer

Because the definition of an exponential

Question 7

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 .
-$\log _{\mathrm{x}} \mathrm{x}+\log _{\mathrm{x}} \mathrm{y}$

Accepted Answer

A)  $\log _{x}(x+y)$ 
B)  $\log _{x} x y$ 
C)  $\log _{x} \frac{x}{y}$ 
D)  $\log _{\mathrm{x}} \mathrm{x} \cdot \log _{\mathrm{x}} \mathrm{y}$ 
A)  $\log _{x}(x+y)$ 
B)  $\log _{x} x y$ 
C)  $\log _{x} \frac{x}{y}$ 
D)  $\log _{\mathrm{x}} \mathrm{x} \cdot \log _{\mathrm{x}} \mathrm{y}$

Question 8

Find the logarithm. Give an approximation to four decimal places
-$\log \left(6.38 \times 10^{4}\right)$

Accepted Answer

A)  4.0003 
B)  4.8048 
C)  0.8048 
D)  -3.1952 
A)  4.0003 
B)  4.8048 
C)  0.8048 
D)  -3.1952

Question 9

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers.
-$\log _{5} \frac{11 \sqrt{x}}{y}$

Accepted Answer

A)  $\log _{5} 11 \cdot \frac{1}{2} \log _{5} \mathrm{~m} \div \log _{5} \mathrm{y}$ 
B)  $\log _{5} y-\log _{5} 11-\frac{1}{2} \log _{5} x$ 
C)  $\log _{5}(11 \sqrt{x})-\log _{5} y$ 
D)  $\log _{5} 11+\frac{1}{2} \log _{5} x-\log _{5} y$ 
A)  $\log _{5} 11 \cdot \frac{1}{2} \log _{5} \mathrm{~m} \div \log _{5} \mathrm{y}$ 
B)  $\log _{5} y-\log _{5} 11-\frac{1}{2} \log _{5} x$ 
C)  $\log _{5}(11 \sqrt{x})-\log _{5} y$ 
D)  $\log _{5} 11+\frac{1}{2} \log _{5} x-\log _{5} y$

Question 10

Solve the equation. Give the solution to three decimal places.
-$7 \mathrm{x}-1=42$

Accepted Answer

A)  $\{1.921\}$ 
B)  $\{6.273\}$ 
C)  $\{3.921\}$ 
D)  $\{2.921\}$ 
A)  $\{1.921\}$ 
B)  $\{6.273\}$ 
C)  $\{3.921\}$ 
D)  $\{2.921\}$

Question 11

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR.
-Given that $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$, find $\log _{10} \frac{27}{4}$

Accepted Answer

A)  0.0512 
B)  0.8293 
C)  0.2549 
D)  1.8572 
A)  0.0512 
B)  0.8293 
C)  0.2549 
D)  1.8572

Question 12

The number of books in a small library increases according to the function $B=6600 e^{0.05 t}$, where $t$ is measured in years. How many books will the library have after 9 years?

Accepted Answer

A)  18,601 
B)  2289 
C)  5270 
D)  10,351 
A)  18,601 
B)  2289 
C)  5270 
D)  10,351

Question 13

Use a calculator and the change-of-base formula to find the logarithm to four decimal places.
-$\log _{\pi} 200$

Accepted Answer

A)  5.2983 
B)  0.2161 
C)  1.1447 
D)  4.6284 
A)  5.2983 
B)  0.2161 
C)  1.1447 
D)  4.6284

Question 14

Determine whether or not the function is one-to-one.
-$\{(-8,-18),(-17,-18),(-10,-4)\}$

Accepted Answer

A) True 
 B)False

Question 15

Solve the equation. Give the exact solution or solutions.
-$\log _{3}(8 x-3)=2$

Accepted Answer

A)  $\left\{\frac{3}{2}\right\}$ 
B)  $\{4\}$ 
C)  $\left\{\frac{12}{5}\right\}$ 
D)  $\left\{\frac{\log _{3} 2+3}{8}\right\}$ 
A)  $\left\{\frac{3}{2}\right\}$ 
B)  $\{4\}$ 
C)  $\left\{\frac{12}{5}\right\}$ 
D)  $\left\{\frac{\log _{3} 2+3}{8}\right\}$

Question 16

An accountant tabulated a firm's profits for four recent years in the following table:
 
The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2001.

Accepted Answer

A)  About \$1,000,000 
B)  About $\$ 750,000$ 
C)  About \$1,300,000 
D)  About $\$ 300,000$ 
A)  About \$1,000,000 
B)  About $\$ 750,000$ 
C)  About \$1,300,000 
D)  About $\$ 300,000$

Question 17

Use a property of logarithms to evaluate $\log _{2} 2^{14}$.

Accepted Answer

A)  $\frac{1}{2}$ 
B)  $\frac{1}{14}$ 
C)  2 
D)  14 
A)  $\frac{1}{2}$ 
B)  $\frac{1}{14}$ 
C)  2 
D)  14

Question 18

Explain why this sequence of steps is incorrect.
$$\begin{aligned}
\log _{3} 121 & =\log _{3}[(-11)(-11)] \
& =\log _{3}(-11)+\log _{3}(-11)
\end{aligned}$$

Accepted Answer

The product rule for logarithms cannot b

Question 19

Explain how this statement needs to be changed so that it is true.
$$\log _{3}(12+12)=\log _{3} 12+\log _{3} 12$$

Accepted Answer

Answers may vary, but the easiest altera

Question 20

Why is finding the value of a $\left(\log _{a} 12\right)$ like answering the question "What is the name of the boy whose name is John?"

Accepted Answer

Answers may vary. One possibility:
Just

Find the logarithm. Give an approximation to four decimal places - $\log 117$

Solve the equation. Give the solution to three decimal places. - $5^{\mathrm{x}+3}=10^{\mathrm{x}-4}$

A student claims that since $\log _{b} x=a$ is not defined for negative values of $x$ , then a must also not be negative. What is wrong with this statement?

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 . - $\log _{\mathrm{q}} 6+\log _{\mathrm{q}} \mathrm{r}$

Sumi Kato's savings account has a balance of $\$ 715$ . After 21 years, what will the amount of interest be at $4.5 \%$ compounded annually?

Why can't we call $\mathrm{y}=(-2)^{\mathrm{x}}$ an exponential function?

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 . - $\log _{\mathrm{x}} \mathrm{x}+\log _{\mathrm{x}} \mathrm{y}$

Find the logarithm. Give an approximation to four decimal places - $\log \left(6.38 \times 10^{4}\right)$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{5} \frac{11 \sqrt{x}}{y}$

Solve the equation. Give the solution to three decimal places. - $7 \mathrm{x}-1=42$

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR. -Given that $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$ , find $\log _{10} \frac{27}{4}$

The number of books in a small library increases according to the function $B=6600 e^{0.05 t}$ , where $t$ is measured in years. How many books will the library have after 9 years?

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - $\log _{\pi} 200$

Determine whether or not the function is one-to-one. - $\{(-8,-18),(-17,-18),(-10,-4)\}$

Solve the equation. Give the exact solution or solutions. - $\log _{3}(8 x-3)=2$

An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2001.

Use a property of logarithms to evaluate $\log _{2} 2^{14}$ .

Explain why this sequence of steps is incorrect. 121 =[(-11)(-11)] =(-11)+(-11)

Explain how this statement needs to be changed so that it is true. $\log _{3}(12+12)=\log _{3} 12+\log _{3} 12$

Why is finding the value of a $\left(\log _{a} 12\right)$ like answering the question "What is the name of the boy whose name is John?"

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

Find the logarithm. Give an approximation to four decimal places - log⁡117\log 117log117

Solve the equation. Give the solution to three decimal places. - 5x+3=10x−45^{\mathrm{x}+3}=10^{\mathrm{x}-4}5x+3=10x−4

A student claims that since log⁡bx=a\log _{b} x=alogb​x=a is not defined for negative values of xxx , then a must also not be negative. What is wrong with this statement?

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⁡q6+log⁡qr\log _{\mathrm{q}} 6+\log _{\mathrm{q}} \mathrm{r}logq​6+logq​r

Sumi Kato's savings account has a balance of $715\$ 715$715 . After 21 years, what will the amount of interest be at 4.5%4.5 \%4.5% compounded annually?

Why can't we call y=(−2)x\mathrm{y}=(-2)^{\mathrm{x}}y=(−2)x an exponential function?

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⁡xx+log⁡xy\log _{\mathrm{x}} \mathrm{x}+\log _{\mathrm{x}} \mathrm{y}logx​x+logx​y

Find the logarithm. Give an approximation to four decimal places - log⁡(6.38×104)\log \left(6.38 \times 10^{4}\right)log(6.38×104)

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - log⁡511xy\log _{5} \frac{11 \sqrt{x}}{y}log5​y11x​​

Solve the equation. Give the solution to three decimal places. - 7x−1=427 \mathrm{x}-1=427x−1=42

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR. -Given that log⁡102=0.3010\log _{10} 2=0.3010log10​2=0.3010 and log⁡103=0.4771\log _{10} 3=0.4771log10​3=0.4771 , find log⁡10274\log _{10} \frac{27}{4}log10​427​

The number of books in a small library increases according to the function B=6600e0.05tB=6600 e^{0.05 t}B=6600e0.05t , where ttt is measured in years. How many books will the library have after 9 years?

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - log⁡π200\log _{\pi} 200logπ​200

Determine whether or not the function is one-to-one. - {(−8,−18),(−17,−18),(−10,−4)}\{(-8,-18),(-17,-18),(-10,-4)\}{(−8,−18),(−17,−18),(−10,−4)}

Solve the equation. Give the exact solution or solutions. - log⁡3(8x−3)=2\log _{3}(8 x-3)=2log3​(8x−3)=2

An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2001.

Use a property of logarithms to evaluate log⁡2214\log _{2} 2^{14}log2​214 .

Explain why this sequence of steps is incorrect. 121 =[(-11)(-11)] =(-11)+(-11)

Explain how this statement needs to be changed so that it is true. log⁡3(12+12)=log⁡312+log⁡312\log _{3}(12+12)=\log _{3} 12+\log _{3} 12log3​(12+12)=log3​12+log3​12

Why is finding the value of a (log⁡a12)\left(\log _{a} 12\right)(loga​12) like answering the question "What is the name of the boy whose name is John?"

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

Find the logarithm. Give an approximation to four decimal places - $\log 117$

Solve the equation. Give the solution to three decimal places. - $5^{\mathrm{x}+3}=10^{\mathrm{x}-4}$

A student claims that since $\log _{b} x=a$ is not defined for negative values of $x$ , then a must also not be negative. What is wrong with this statement?

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 . - $\log _{\mathrm{q}} 6+\log _{\mathrm{q}} \mathrm{r}$

Sumi Kato's savings account has a balance of $\$ 715$ . After 21 years, what will the amount of interest be at $4.5 \%$ compounded annually?

Why can't we call $\mathrm{y}=(-2)^{\mathrm{x}}$ an exponential function?

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 . - $\log _{\mathrm{x}} \mathrm{x}+\log _{\mathrm{x}} \mathrm{y}$

Find the logarithm. Give an approximation to four decimal places - $\log \left(6.38 \times 10^{4}\right)$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{5} \frac{11 \sqrt{x}}{y}$

Solve the equation. Give the solution to three decimal places. - $7 \mathrm{x}-1=42$

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR. -Given that $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$ , find $\log _{10} \frac{27}{4}$

The number of books in a small library increases according to the function $B=6600 e^{0.05 t}$ , where $t$ is measured in years. How many books will the library have after 9 years?

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - $\log _{\pi} 200$

Determine whether or not the function is one-to-one. - $\{(-8,-18),(-17,-18),(-10,-4)\}$

Solve the equation. Give the exact solution or solutions. - $\log _{3}(8 x-3)=2$

Use a property of logarithms to evaluate $\log _{2} 2^{14}$ .

Explain how this statement needs to be changed so that it is true. $\log _{3}(12+12)=\log _{3} 12+\log _{3} 12$

Why is finding the value of a $\left(\log _{a} 12\right)$ like answering the question "What is the name of the boy whose name is John?"