Question 1

Find the logarithm. Give an approximation to four decimal places
-$\ln 40,500,000$

Accepted Answer

A)  0.0569 
B)  17.5168 
C)  7.6075 
D)  6.0039 
A)  0.0569 
B)  17.5168 
C)  7.6075 
D)  6.0039

Question 2

Find the indicated value.
-Let $f(x)=3^{x} \cdot f(4)$

Accepted Answer

A)  27 
B)  81 
C)  243 
D)  12 
A)  27 
B)  81 
C)  243 
D)  12

Question 3

Logarithms simplify calculations by changing multiplication to

Accepted Answer

The answer of Logarithms simplify calculations by changing multiplication to...

Question 4

Why is evaluating $\ln \mathrm{e}^{\mathrm{a}}$ much like answering the question "What is the name of the boy whose name is Jose?"

Accepted Answer

Answers may vary. One possibility:
As in

Question 5

Find the logarithm. Give an approximation to four decimal places
-$\log 2.35$

Accepted Answer

A)  0.8544 
B)  0.3522 
C)  0.3711 
D)  0.3892 
A)  0.8544 
B)  0.3522 
C)  0.3711 
D)  0.3892

Question 6

Give a definition for the following term: quotient rule of logarithms .

Accepted Answer

For base @#LAT-DLM&,

Question 7

What is the connection between $e^{x}$ and $\ln x$ ?

Accepted Answer

Answers may vary. On

Question 8

Write in logarithmic form.
-$64^{-4 / 3}=\frac{1}{256}$

Accepted Answer

A)  $\log _{64}\left(\frac{4}{3}\right)=-\frac{1}{256}$ 
B)  $\log _{256} 64=-\frac{4}{3}$ 
C)  $\log _{64}\left(\frac{1}{256}\right)=-\frac{4}{3}$ 
D)  $\log _{4 / 3} 256=64$ 
A)  $\log _{64}\left(\frac{4}{3}\right)=-\frac{1}{256}$ 
B)  $\log _{256} 64=-\frac{4}{3}$ 
C)  $\log _{64}\left(\frac{1}{256}\right)=-\frac{4}{3}$ 
D)  $\log _{4 / 3} 256=64$

Question 9

Is the logarithm to the base 3 of 5 written as " $\log _{5} 3$ " or" $\log _{3} 5 "$ ?

Accepted Answer

The answer of Is the logarithm to the base 3...

Question 10

Solve the equation. Give the exact solution or solutions.
-$\log _{4}(\mathrm{x}+2)+\log _{4}(\mathrm{x}-2)=3$

Accepted Answer

A)  $\left\{\frac{19}{4}\right\}$ 
B)  $\{68\}$ 
C)  $\{2 \sqrt{17}\}$ 
D)  $\left\{\frac{64}{3}\right\}$ 
A)  $\left\{\frac{19}{4}\right\}$ 
B)  $\{68\}$ 
C)  $\{2 \sqrt{17}\}$ 
D)  $\left\{\frac{64}{3}\right\}$

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 .
-$\log _{2} 13+\log _{2} 11$

Accepted Answer

A)  $\log _{2} 24$ 
B)  $\log _{4} 143$ 
C)  $\log _{4} 24$ 
D)  $\log _{2} 143$ 
A)  $\log _{2} 24$ 
B)  $\log _{4} 143$ 
C)  $\log _{4} 24$ 
D)  $\log _{2} 143$

Question 12

Solve the equation.
-$27^{x}=81(3 x-1)$

Accepted Answer

A)  $\frac{1}{2}$ 
B)  $-\frac{4}{9}$ 
C)  $\frac{1}{9}$ 
D)  $\frac{4}{9}$ 
A)  $\frac{1}{2}$ 
B)  $-\frac{4}{9}$ 
C)  $\frac{1}{9}$ 
D)  $\frac{4}{9}$

Question 13

Solve the equation. Give the exact solution or solutions.
-$\log _{6} x^{2}=\log _{6}(2 x+15)$

Accepted Answer

A)  $\varnothing$ 
B)  $\{5,-3\}$ 
C)  $\{-3\}$ 
D)  $\{5\}$ 
A)  $\varnothing$ 
B)  $\{5,-3\}$ 
C)  $\{-3\}$ 
D)  $\{5\}$

Question 14

Find the amount of money in an account after 6 years if $\$ 3900$ is deposited at $4 \%$ annual interest compounded quarterly.

Accepted Answer

A)  $\$ 4946.14$ 
B)  $\$ 4955.89$ 
C)  $\$ 4951.97$ 
D)  $\$ 4934.74$ 
A)  $\$ 4946.14$ 
B)  $\$ 4955.89$ 
C)  $\$ 4951.97$ 
D)  $\$ 4934.74$

Question 15

The time $t$ in years for an amount increasing at a rate $r$ (in decimal form) to double is given by $t(r)=\frac{\ln 2}{\ln (1+r)}$. This is called "doubling time." How long will it take for prices in the economy to double at a $4 \%$ annual inflation rate? Round to the nearest year.

Accepted Answer

A)  $14 \mathrm{yr}$ 
B)  $18 \mathrm{yr}$ 
C)  $28 \mathrm{yr}$ 
D)  $23 \mathrm{yr}$ 
A)  $14 \mathrm{yr}$ 
B)  $18 \mathrm{yr}$ 
C)  $28 \mathrm{yr}$ 
D)  $23 \mathrm{yr}$

Question 16

Find the logarithm. Give an approximation to four decimal places
-$\ln 39$

Accepted Answer

A)  0.2721 
B)  1.5911 
C)  3.6636 
D)  14.3911 
A)  0.2721 
B)  1.5911 
C)  3.6636 
D)  14.3911

Question 17

Solve the equation.
-$2(7+3 x)=\frac{1}{4}$

Accepted Answer

A)  $\{4\}$ 
B)  $\{3\}$ 
C)  $\{-3\}$ 
D)  $\left\{\frac{1}{2}\right\}$ 
A)  $\{4\}$ 
B)  $\{3\}$ 
C)  $\{-3\}$ 
D)  $\left\{\frac{1}{2}\right\}$

Question 18

Solve the equation.
-$4(7-3 x)=\frac{1}{16}$

Accepted Answer

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

Question 19

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.
-$f(x)=-4 x$

Accepted Answer

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

Question 20

Solve the equation. Give the exact solution or solutions.
-$\log 9(x-6)+\log 9(x-6)=1$

Accepted Answer

A)  $\{9\}$ 
B)  $\{-\sqrt{37}, \sqrt{37}\}$ 
C)  $\{-9,9\}$ 
D)  $\{\sqrt{37}\}$ 
A)  $\{9\}$ 
B)  $\{-\sqrt{37}, \sqrt{37}\}$ 
C)  $\{-9,9\}$ 
D)  $\{\sqrt{37}\}$

Find the logarithm. Give an approximation to four decimal places - $\ln 40,500,000$

Find the indicated value. -Let $f(x)=3^{x} \cdot f(4)$

Logarithms simplify calculations by changing multiplication to

Why is evaluating $\ln \mathrm{e}^{\mathrm{a}}$ much like answering the question "What is the name of the boy whose name is Jose?"

Find the logarithm. Give an approximation to four decimal places - $\log 2.35$

Give a definition for the following term: quotient rule of logarithms .

What is the connection between $e^{x}$ and $\ln x$ ?

Write in logarithmic form. - $64^{-4 / 3}=\frac{1}{256}$

Is the logarithm to the base 3 of 5 written as " $\log _{5} 3$ " or" $\log _{3} 5 "$ ?

Solve the equation. Give the exact solution or solutions. - $\log _{4}(\mathrm{x}+2)+\log _{4}(\mathrm{x}-2)=3$

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 . - $\log _{2} 13+\log _{2} 11$

Solve the equation. - $27^{x}=81(3 x-1)$

Solve the equation. Give the exact solution or solutions. - $\log _{6} x^{2}=\log _{6}(2 x+15)$

Find the amount of money in an account after 6 years if $\$ 3900$ is deposited at $4 \%$ annual interest compounded quarterly.

The time $t$ in years for an amount increasing at a rate $r$ (in decimal form) to double is given by $t(r)=\frac{\ln 2}{\ln (1+r)}$ . This is called "doubling time." How long will it take for prices in the economy to double at a $4 \%$ annual inflation rate? Round to the nearest year.

Find the logarithm. Give an approximation to four decimal places - $\ln 39$

Solve the equation. - $2(7+3 x)=\frac{1}{4}$

Solve the equation. - $4(7-3 x)=\frac{1}{16}$

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. - $f(x)=-4 x$

Solve the equation. Give the exact solution or solutions. - $\log 9(x-6)+\log 9(x-6)=1$

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 - ln⁡40,500,000\ln 40,500,000ln40,500,000

Find the indicated value. -Let f(x)=3x⋅f(4)f(x)=3^{x} \cdot f(4)f(x)=3x⋅f(4)

Logarithms simplify calculations by changing multiplication to

Why is evaluating ln⁡ea\ln \mathrm{e}^{\mathrm{a}}lnea much like answering the question "What is the name of the boy whose name is Jose?"

Find the logarithm. Give an approximation to four decimal places - log⁡2.35\log 2.35log2.35

Give a definition for the following term: quotient rule of logarithms .

What is the connection between exe^{x}ex and ln⁡x\ln xlnx ?

Write in logarithmic form. - 64−4/3=125664^{-4 / 3}=\frac{1}{256}64−4/3=2561​

Is the logarithm to the base 3 of 5 written as " log⁡53\log _{5} 3log5​3 " or" log⁡35"\log _{3} 5 "log3​5" ?

Solve the equation. Give the exact solution or solutions. - log⁡4(x+2)+log⁡4(x−2)=3\log _{4}(\mathrm{x}+2)+\log _{4}(\mathrm{x}-2)=3log4​(x+2)+log4​(x−2)=3

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⁡213+log⁡211\log _{2} 13+\log _{2} 11log2​13+log2​11

Solve the equation. - 27x=81(3x−1)27^{x}=81(3 x-1)27x=81(3x−1)

Solve the equation. Give the exact solution or solutions. - log⁡6x2=log⁡6(2x+15)\log _{6} x^{2}=\log _{6}(2 x+15)log6​x2=log6​(2x+15)

Find the amount of money in an account after 6 years if $3900\$ 3900$3900 is deposited at 4%4 \%4% annual interest compounded quarterly.

Find the logarithm. Give an approximation to four decimal places - ln⁡39\ln 39ln39

Solve the equation. - 2(7+3x)=142(7+3 x)=\frac{1}{4}2(7+3x)=41​

Solve the equation. - 4(7−3x)=1164(7-3 x)=\frac{1}{16}4(7−3x)=161​

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)=−4xf(x)=-4 xf(x)=−4x

Solve the equation. Give the exact solution or solutions. - log⁡9(x−6)+log⁡9(x−6)=1\log 9(x-6)+\log 9(x-6)=1log9(x−6)+log9(x−6)=1

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 - $\ln 40,500,000$

Find the indicated value. -Let $f(x)=3^{x} \cdot f(4)$

Why is evaluating $\ln \mathrm{e}^{\mathrm{a}}$ much like answering the question "What is the name of the boy whose name is Jose?"

Find the logarithm. Give an approximation to four decimal places - $\log 2.35$

What is the connection between $e^{x}$ and $\ln x$ ?

Write in logarithmic form. - $64^{-4 / 3}=\frac{1}{256}$

Is the logarithm to the base 3 of 5 written as " $\log _{5} 3$ " or" $\log _{3} 5 "$ ?

Solve the equation. Give the exact solution or solutions. - $\log _{4}(\mathrm{x}+2)+\log _{4}(\mathrm{x}-2)=3$

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 . - $\log _{2} 13+\log _{2} 11$

Solve the equation. - $27^{x}=81(3 x-1)$

Solve the equation. Give the exact solution or solutions. - $\log _{6} x^{2}=\log _{6}(2 x+15)$

Find the amount of money in an account after 6 years if $\$ 3900$ is deposited at $4 \%$ annual interest compounded quarterly.

Find the logarithm. Give an approximation to four decimal places - $\ln 39$

Solve the equation. - $2(7+3 x)=\frac{1}{4}$

Solve the equation. - $4(7-3 x)=\frac{1}{16}$

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. - $f(x)=-4 x$

Solve the equation. Give the exact solution or solutions. - $\log 9(x-6)+\log 9(x-6)=1$