Question 1

$\log _{17}(7-15)=\log _{17} 7-\log _{17} 15$

Accepted Answer

A) True 
 B)False

Question 2

Solve the equation.
-$\log 1 / 2 x=-3$

Accepted Answer

A)  $\left\{\frac{1}{9}\right\}$ 
B)  $\{8\}$ 
C)  $\left\{\frac{1}{8}\right\}$ 
D)  $\{9\}$ 
A)  $\left\{\frac{1}{9}\right\}$ 
B)  $\{8\}$ 
C)  $\left\{\frac{1}{8}\right\}$ 
D)  $\{9\}$

Question 3

Graph the function.
-$f(x)=\left(\frac{1}{4}\right)^{x}$

Accepted Answer

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

Question 4

Write in logarithmic form.
-$\left(\frac{7}{5}\right)^{5}=\frac{16,807}{3125}$

Accepted Answer

A)  $\log _{5}\left(\frac{7}{5}\right)=\frac{16,807}{3125}$ 
B)  $\log _{7 / 5} 5=\frac{16,807}{3125}$ 
C)  $\frac{\log _{5} 16,807}{\log _{5} 3125}=\frac{7}{5}$ 
D)  $\log _{7 / 5}\left(\frac{16,807}{3125}\right)=5$ 
A)  $\log _{5}\left(\frac{7}{5}\right)=\frac{16,807}{3125}$ 
B)  $\log _{7 / 5} 5=\frac{16,807}{3125}$ 
C)  $\frac{\log _{5} 16,807}{\log _{5} 3125}=\frac{7}{5}$ 
D)  $\log _{7 / 5}\left(\frac{16,807}{3125}\right)=5$

Question 5

Write in exponential form.
-$\log _{3} 1=x$

Accepted Answer

A)  $\{3\}$ 
B)  $\{0\}$ 
C)  $\{9\}$ 
D)  $\{1\}$ 
A)  $\{3\}$ 
B)  $\{0\}$ 
C)  $\{9\}$ 
D)  $\{1\}$

Question 6

$\log _{3}(6+6)=\log _{3} 6+\log _{3} 6$

Accepted Answer

A) True 
 B)False

Question 7

What is the domain of the function $y=\left(\frac{1}{5}\right)^{x}$ ?

Accepted Answer

A)  $(\infty, \infty)$ 
B)  $(0, \infty)$ 
C)  $(\infty, 0)$ 
D)  $[0, \infty)$ 
A)  $(\infty, \infty)$ 
B)  $(0, \infty)$ 
C)  $(\infty, 0)$ 
D)  $[0, \infty)$

Question 8

The number of acres in a landfill is given by the function $B=9500 e^{-0.04 t}$, where $t$ is measured in years. How many acres will the landfill have after 3 years? (Round to the nearest acre.)

Accepted Answer

A)  8748 
B)  8426 
C)  20,143 
D)  7206 
A)  8748 
B)  8426 
C)  20,143 
D)  7206

Question 9

Solve the equation.
-$\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$

Accepted Answer

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

Question 10

The sales of a new product (in items per month) can be approximated by $S(x)=225+100 \log _{10}(3 t+1)$, where $t$ represents the number of months after the item first becomes available. Find the number of items sold per month 3 months after the item first becomes available.

Accepted Answer

A)  2225 items per month 
B)  1225 items per month 
C)  425 items per month 
D)  325 items per month 
A)  2225 items per month 
B)  1225 items per month 
C)  425 items per month 
D)  325 items per month

Question 11

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$f(x)=3 x^{3}-6$

Accepted Answer

A)  $f^{-1}(x)=\sqrt[3]{\frac{x+6}{3}}$ 
B)  Not one-to-one 
C)  $f^{-1}(x)=\sqrt[3]{\frac{x-6}{3}}$ 
D)  $f^{-1}(x)=\sqrt[3]{\frac{x}{3}}+6$ 
A)  $f^{-1}(x)=\sqrt[3]{\frac{x+6}{3}}$ 
B)  Not one-to-one 
C)  $f^{-1}(x)=\sqrt[3]{\frac{x-6}{3}}$ 
D)  $f^{-1}(x)=\sqrt[3]{\frac{x}{3}}+6$

Question 12

Write in exponential form.
-$\log _{10} x=1$

Accepted Answer

A)  $\{0\}$ 
B)  $ \{10\}$ 
C)  $\left\{\frac{1}{10}\right\}$ 
D)  $\{1\}$ 
A)  $\{0\}$ 
B)  $ \{10\}$ 
C)  $\left\{\frac{1}{10}\right\}$ 
D)  $\{1\}$

Question 13

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated.
-$\ln \mathrm{e}^{3 \mathrm{x}}=\pi \quad$ (Give the exact solution.)

Accepted Answer

A)  $\{3 \pi\}$ 
B)  $\{\pi-3\}$ 
C)  $\left\{\frac{\pi}{3 e}\right\}$ 
D)  $\left\{\frac{\pi}{3}\right\}$ 
A)  $\{3 \pi\}$ 
B)  $\{\pi-3\}$ 
C)  $\left\{\frac{\pi}{3 e}\right\}$ 
D)  $\left\{\frac{\pi}{3}\right\}$

Question 14

Solve the equation.
-$x=\log _{27} 3$

Accepted Answer

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

Question 15

Use a property of logarithms to evaluate $6^{\log _{6} 16}$.

Accepted Answer

A)  $\frac{1}{16}$ 
B)  6 
C)  $\frac{1}{6}$ 
D)  16 
A)  $\frac{1}{16}$ 
B)  6 
C)  $\frac{1}{6}$ 
D)  16

Question 16

Express as a product.
-$\log _{2} 2^{5}$

Accepted Answer

A)  $5 \log _{2} 2^{5}$ 
B)  $5 \log _{2} 2$ 
C)  $2 \log _{5} 2^{5}$ 
D)  $2 \log _{5} 2$ 
A)  $5 \log _{2} 2^{5}$ 
B)  $5 \log _{2} 2$ 
C)  $2 \log _{5} 2^{5}$ 
D)  $2 \log _{5} 2$

Question 17

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 linear graph to estimate the profits in the year 2001.

Accepted Answer

A)  About $\$ 700,000$ 
B)  About $\$ 800,000$ 
C)  About $\$ 500,000$ 
D)  About $\$ 900,000$ 
A)  About $\$ 700,000$ 
B)  About $\$ 800,000$ 
C)  About $\$ 500,000$ 
D)  About $\$ 900,000$

Question 18

Determine whether or not the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 19

Suppose $\$ 9000$ is invested at $7.25 \%$ annual interest, compounded continually. (i) What will be the amount in the account in 6 years if no money is withdrawn? (ii) How long will it take for the initial principal to double? Round to the nearest tenth of a year.

Accepted Answer

A)  $\$ 9676.74$; (ii) 15.2 years 
B)  $\$ 9000.00$; (ii) 12.6 years 
C)  $\$ 4018.03$; (ii) 5.6 years 
D)  (i) $\$ 13,904.67$; (ii) 9.6 years 
A)  $\$ 9676.74$; (ii) 15.2 years 
B)  $\$ 9000.00$; (ii) 12.6 years 
C)  $\$ 4018.03$; (ii) 5.6 years 
D)  (i) $\$ 13,904.67$; (ii) 9.6 years

Question 20

The amount of particulate matter left in solution during a filtering process decreases by the equation $P=200(0.5)^{0.4 n}$, where $\mathrm{n}$ is the number of filtering steps. Find the amounts left for $\mathrm{n}=0$ and $\mathrm{n}=5$. (Round to the nearest whole number.)

Accepted Answer

A)  200,800 
B)  200,6 
C)  200,50 
D)  400,50 
A)  200,800 
B)  200,6 
C)  200,50 
D)  400,50

$\log _{17}(7-15)=\log _{17} 7-\log _{17} 15$

Solve the equation. - $\log 1 / 2 x=-3$

Graph the function. - $f(x)=\left(\frac{1}{4}\right)^{x}$ $Graph the function. - f(x)=\left(\frac{1}{4}\right)^{x}$

Write in logarithmic form. - $\left(\frac{7}{5}\right)^{5}=\frac{16,807}{3125}$

Write in exponential form. - $\log _{3} 1=x$

$\log _{3}(6+6)=\log _{3} 6+\log _{3} 6$

What is the domain of the function $y=\left(\frac{1}{5}\right)^{x}$ ?

The number of acres in a landfill is given by the function $B=9500 e^{-0.04 t}$ , where $t$ is measured in years. How many acres will the landfill have after 3 years? (Round to the nearest acre.)

Solve the equation. - $\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$

The sales of a new product (in items per month) can be approximated by $S(x)=225+100 \log _{10}(3 t+1)$ , where $t$ represents the number of months after the item first becomes available. Find the number of items sold per month 3 months after the item first becomes available.

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x)=3 x^{3}-6$

Write in exponential form. - $\log _{10} x=1$

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\ln \mathrm{e}^{3 \mathrm{x}}=\pi \quad$ (Give the exact solution.)

Solve the equation. - $x=\log _{27} 3$

Use a property of logarithms to evaluate $6^{\log _{6} 16}$ .

Express as a product. - $\log _{2} 2^{5}$

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 linear graph to estimate the profits in the year 2001.

Determine whether or not the function is one-to-one. -

Suppose $\$ 9000$ is invested at $7.25 \%$ annual interest, compounded continually. (i) What will be the amount in the account in 6 years if no money is withdrawn? (ii) How long will it take for the initial principal to double? Round to the nearest tenth of a year.

The amount of particulate matter left in solution during a filtering process decreases by the equation $P=200(0.5)^{0.4 n}$ , where $\mathrm{n}$ is the number of filtering steps. Find the amounts left for $\mathrm{n}=0$ and $\mathrm{n}=5$ . (Round to the nearest whole number.)

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

log⁡17(7−15)=log⁡177−log⁡1715\log _{17}(7-15)=\log _{17} 7-\log _{17} 15log17​(7−15)=log17​7−log17​15

Solve the equation. - log⁡1/2x=−3\log 1 / 2 x=-3log1/2x=−3

Graph the function. - f(x)=(14)xf(x)=\left(\frac{1}{4}\right)^{x}f(x)=(41​)x

Write in logarithmic form. - (75)5=16,8073125\left(\frac{7}{5}\right)^{5}=\frac{16,807}{3125}(57​)5=312516,807​

Write in exponential form. - log⁡31=x\log _{3} 1=xlog3​1=x

log⁡3(6+6)=log⁡36+log⁡36\log _{3}(6+6)=\log _{3} 6+\log _{3} 6log3​(6+6)=log3​6+log3​6

What is the domain of the function y=(15)xy=\left(\frac{1}{5}\right)^{x}y=(51​)x ?

The number of acres in a landfill is given by the function B=9500e−0.04tB=9500 e^{-0.04 t}B=9500e−0.04t , where ttt is measured in years. How many acres will the landfill have after 3 years? (Round to the nearest acre.)

Solve the equation. - (25)x=1258\left(\frac{2}{5}\right)^{x}=\frac{125}{8}(52​)x=8125​

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - f(x)=3x3−6f(x)=3 x^{3}-6f(x)=3x3−6

Write in exponential form. - log⁡10x=1\log _{10} x=1log10​x=1

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - ln⁡e3x=π\ln \mathrm{e}^{3 \mathrm{x}}=\pi \quadlne3x=π (Give the exact solution.)

Solve the equation. - x=log⁡273x=\log _{27} 3x=log27​3

Use a property of logarithms to evaluate 6log⁡6166^{\log _{6} 16}6log6​16 .

Express as a product. - log⁡225\log _{2} 2^{5}log2​25

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 linear graph to estimate the profits in the year 2001.

Determine whether or not the function is one-to-one. -

Suppose $9000\$ 9000$9000 is invested at 7.25%7.25 \%7.25% annual interest, compounded continually. (i) What will be the amount in the account in 6 years if no money is withdrawn? (ii) How long will it take for the initial principal to double? Round to the nearest tenth of a year.

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

$\log _{17}(7-15)=\log _{17} 7-\log _{17} 15$

Solve the equation. - $\log 1 / 2 x=-3$

Graph the function. - $f(x)=\left(\frac{1}{4}\right)^{x}$ $Graph the function. - f(x)=\left(\frac{1}{4}\right)^{x}$

Write in logarithmic form. - $\left(\frac{7}{5}\right)^{5}=\frac{16,807}{3125}$

Write in exponential form. - $\log _{3} 1=x$

$\log _{3}(6+6)=\log _{3} 6+\log _{3} 6$

What is the domain of the function $y=\left(\frac{1}{5}\right)^{x}$ ?

The number of acres in a landfill is given by the function $B=9500 e^{-0.04 t}$ , where $t$ is measured in years. How many acres will the landfill have after 3 years? (Round to the nearest acre.)

Solve the equation. - $\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x)=3 x^{3}-6$

Write in exponential form. - $\log _{10} x=1$

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\ln \mathrm{e}^{3 \mathrm{x}}=\pi \quad$ (Give the exact solution.)

Solve the equation. - $x=\log _{27} 3$

Use a property of logarithms to evaluate $6^{\log _{6} 16}$ .

Express as a product. - $\log _{2} 2^{5}$

Suppose $\$ 9000$ is invested at $7.25 \%$ annual interest, compounded continually. (i) What will be the amount in the account in 6 years if no money is withdrawn? (ii) How long will it take for the initial principal to double? Round to the nearest tenth of a year.