Question 1

Graph the function and its inverse on the same set of axes.
-f(x) = 3x

Accepted Answer

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

Question 2

Find the exact value.
-$\ln e ^ { 6 }$

Accepted Answer

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

Question 3

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-

Accepted Answer

A) 
  
B)  not one-to-one 
C) 
  
D) 
  
A) 
  
B)  not one-to-one 
C) 
  
D) 
  C

Question 4

Solve.
-Use the formula $R = \log \left( \frac { a } { T } \right) + B$ to find the intensity $R$ on the Richter scale, given that amplitude $a$ is 426 micrometers, time T between waves is $3.3$ seconds, and B is 2.1. Round answer to one decimal place.

Accepted Answer

A)  $2.1$ 
B)  $7.2$ 
C)  $4.2$ 
D)  7 
A)  $2.1$ 
B)  $7.2$ 
C)  $4.2$ 
D)  7

Question 5

Write as an exponential equation.
-$\log _ { 14 } \sqrt [ 5 ] { 14 } = \frac { 1 } { 5 }$

Accepted Answer

A)  $14 ^ { 1 / 5 } = \sqrt [ 5 ] { 14 }$ 
B)  $( \sqrt [ 5 ] { 14 } ) ^ { 1 / 5 } = 14$ 
C)  $14 ^ { \sqrt [ 5 ] { 14 } } = \frac { 1 } { 5 }$ 
D)  $\left( \frac { 1 } { 5 } \right) ^ { 14 } = \sqrt [ 5 ] { 14 }$ 
A)  $14 ^ { 1 / 5 } = \sqrt [ 5 ] { 14 }$ 
B)  $( \sqrt [ 5 ] { 14 } ) ^ { 1 / 5 } = 14$ 
C)  $14 ^ { \sqrt [ 5 ] { 14 } } = \frac { 1 } { 5 }$ 
D)  $\left( \frac { 1 } { 5 } \right) ^ { 14 } = \sqrt [ 5 ] { 14 }$

Question 6

Solve the equation.
-$3 ^{( 12 - 2 x )} = 6561$

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  $- 2$ 
A)  1 
B)  2 
C)  3 
D)  $- 2$

Question 7

Solve. Round the answer to the nearest whole number.
-Suppose a city with population of 170,000 has been decreasing at a rate of 2% per year. If this rate continues, predict the population of the city in 10 years.

Accepted Answer

A)  153,745 
B)  207,229 
C)  125,362 
D)  138,902 
A)  153,745 
B)  207,229 
C)  125,362 
D)  138,902

Question 8

Determine whether the functions f and g are inverses of each other.
-$f ( x ) = 2 x + 4 ; g ( x ) = \frac { x - 4 } { 2 }$

Accepted Answer

A) True 
 B)False

Question 9

Solve. Round the answer to the nearest whole number.
-The number of students attending summer school at a local community college has been decreasing each year by $7 \%$. If 761 students currently attend summer school and this rate continues, find the number of students attending summer school in 5 years.

Accepted Answer

A)  559 students 
B)  529 students 
C)  502 students 
D)  531 students 
A)  559 students 
B)  529 students 
C)  502 students 
D)  531 students

Question 10

For the given functions f and g, find the requested function.
-If $f ( x ) = 8 x - 7$ and $g ( x ) = 2 x - 3$, find $( f - g ) ( x )$.

Accepted Answer

A)  $( f - g ) ( x ) = 10 x - 10$ 
B)  $( f - g ) ( x ) = 6 x - 10$ 
C)  $( f - g ) ( x ) = - 6 x + 4$ 
D)  $( f - g ) ( x ) = 6 x - 4$ 
A)  $( f - g ) ( x ) = 10 x - 10$ 
B)  $( f - g ) ( x ) = 6 x - 10$ 
C)  $( f - g ) ( x ) = - 6 x + 4$ 
D)  $( f - g ) ( x ) = 6 x - 4$

Question 11

Graph the function.
-$f(x)=\ln (x+5)$

Accepted Answer

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

Question 12

Determine whether the graph of the function is the graph of a one-to-one function.
-

Accepted Answer

A) True 
 B)False

Question 13

Solve. Round the answer to the nearest whole number.
-The size of the rat population of a wharf area grows at a rate of $5 \%$ monthly. If there are 200 rats in June, find how many rats should be expected by next June.

Accepted Answer

A)  $359 \mathrm { rats }$ 
B)  320 rats 
C)  402 rats 
D)  210 rats 
A)  $359 \mathrm { rats }$ 
B)  320 rats 
C)  402 rats 
D)  210 rats

Question 14

Write as an exponential equation.
-$\log _ { 5 } 125 = 3$

Accepted Answer

A)  $125 ^ { 3 } = 5$ 
B)  $5 ^ { 3 } = 125$ 
C)  $5 ^ { 125 } = 3$ 
D)  $3 ^ { 5 } = 125$ 
A)  $125 ^ { 3 } = 5$ 
B)  $5 ^ { 3 } = 125$ 
C)  $5 ^ { 125 } = 3$ 
D)  $3 ^ { 5 } = 125$

Question 15

Write as a logarithmic equation.
-$2 ^ { - 3 } = \frac { 1 } { 8 }$

Accepted Answer

A)  $\log _ { 1 / 8 } 2 = - 3$ 
B)  $\log _ { 2 } \frac { 1 } { 8 } = - 3$ 
C)  $\log _ { - 3 } \frac { 1 } { 8 } = 2$ 
D)  $\log _ { 2 } - 3 = \frac { 1 } { 8 }$ 
A)  $\log _ { 1 / 8 } 2 = - 3$ 
B)  $\log _ { 2 } \frac { 1 } { 8 } = - 3$ 
C)  $\log _ { - 3 } \frac { 1 } { 8 } = 2$ 
D)  $\log _ { 2 } - 3 = \frac { 1 } { 8 }$

Question 16

Find the exact value.
-$\log 0.0001$

Accepted Answer

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

Question 17

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

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $- 10$ 
C) $-\frac { 5 } { 2 }$ 
D)  10 
A)  $\frac { 1 } { 2 }$ 
B)  $- 10$ 
C) $-\frac { 5 } { 2 }$ 
D)  10

Question 18

Simplify.
-$7 ^ { \log _ { 7 } 15 }$

Accepted Answer

A)  $\log _ { 7 } 15$ 
B)  15 
C)  7 
D)  22 
A)  $\log _ { 7 } 15$ 
B)  15 
C)  7 
D)  22

Question 19

Provide an appropriate response.
-Graph the functions $y = 3 ^ { x }$ and $y = \log _ { 3 } x$ on the same coordinate system.

Accepted Answer

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

Question 20

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { b } x - \log _ { b } y$

Accepted Answer

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

Graph the function and its inverse on the same set of axes. -f(x) = 3x

Find the exact value. - $\ln e ^ { 6 }$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. -

Solve. -Use the formula $R = \log \left( \frac { a } { T } \right) + B$ to find the intensity $R$ on the Richter scale, given that amplitude $a$ is 426 micrometers, time T between waves is $3.3$ seconds, and B is 2.1. Round answer to one decimal place.

Write as an exponential equation. - $\log _ { 14 } \sqrt [ 5 ] { 14 } = \frac { 1 } { 5 }$

Solve the equation. - $3 ^{( 12 - 2 x )} = 6561$

Solve. Round the answer to the nearest whole number. -Suppose a city with population of 170,000 has been decreasing at a rate of 2% per year. If this rate continues, predict the population of the city in 10 years.

Determine whether the functions f and g are inverses of each other. - $f ( x ) = 2 x + 4 ; g ( x ) = \frac { x - 4 } { 2 }$

For the given functions f and g, find the requested function. -If $f ( x ) = 8 x - 7$ and $g ( x ) = 2 x - 3$ , find $( f - g ) ( x )$ .

Graph the function. - $f(x)=\ln (x+5)$ $Graph the function. - f(x)=\ln (x+5)$

Determine whether the graph of the function is the graph of a one-to-one function. -

Solve. Round the answer to the nearest whole number. -The size of the rat population of a wharf area grows at a rate of $5 \%$ monthly. If there are 200 rats in June, find how many rats should be expected by next June.

Write as an exponential equation. - $\log _ { 5 } 125 = 3$

Write as a logarithmic equation. - $2 ^ { - 3 } = \frac { 1 } { 8 }$

Find the exact value. - $\log 0.0001$

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

Simplify. - $7 ^ { \log _ { 7 } 15 }$

Provide an appropriate response. -Graph the functions $y = 3 ^ { x }$ and $y = \log _ { 3 } x$ on the same coordinate system. $Provide an appropriate response. -Graph the functions y = 3 ^ { x } and y = \log _ { 3 } x on the same coordinate system.$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { b } x - \log _ { b } y$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

Graph the function and its inverse on the same set of axes. -f(x) = 3x

Find the exact value. - ln⁡e6\ln e ^ { 6 }lne6

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. -

Solve. -Use the formula R=log⁡(aT)+BR = \log \left( \frac { a } { T } \right) + BR=log(Ta​)+B to find the intensity RRR on the Richter scale, given that amplitude aaa is 426 micrometers, time T between waves is 3.33.33.3 seconds, and B is 2.1. Round answer to one decimal place.

Write as an exponential equation. - log⁡14145=15\log _ { 14 } \sqrt [ 5 ] { 14 } = \frac { 1 } { 5 }log14​514​=51​

Solve the equation. - 3(12−2x)=65613 ^{( 12 - 2 x )} = 65613(12−2x)=6561