Question 1

Find the value of the logarithmic expression.
-$\log _ { 2 } 8$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  6 
C)  3 
D)  1 
A)  $\frac { 1 } { 3 }$ 
B)  6 
C)  3 
D)  1

Question 2

Solve the equation.
-$\log _ { 7 } ( x + 2 ) - \log _ { 7 } x = 2$

Accepted Answer

A)  24 
B)  7 
C)  $\frac { 2 } { 49 }$ 
D)  $\frac { 1 } { 24 }$ 
A)  24 
B)  7 
C)  $\frac { 2 } { 49 }$ 
D)  $\frac { 1 } { 24 }$

Question 3

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { \mathrm { C } } \mathrm { m } + \log _ { \mathrm { C } } \mathrm { n }$

Accepted Answer

A)  $\log _ { \mathrm { C } } \mathrm { mn }$ 
B)  $\log _ { \mathrm { C } } \frac { \mathrm { m } } { \mathrm { n } }$ 
C)  $\log _ { \mathrm { c } } m \cdot \log _ { \mathrm { c } } n$ 
D)  $\log _ { \mathrm { C } } ( \mathrm { m } + \mathrm { n } )$ 
A)  $\log _ { \mathrm { C } } \mathrm { mn }$ 
B)  $\log _ { \mathrm { C } } \frac { \mathrm { m } } { \mathrm { n } }$ 
C)  $\log _ { \mathrm { c } } m \cdot \log _ { \mathrm { c } } n$ 
D)  $\log _ { \mathrm { C } } ( \mathrm { m } + \mathrm { n } )$

Question 4

Solve.
-The size of the beaver population at a national park increases at the rate of $4.2 \%$ per year. If the size of the current population is 101 , find how many beavers there should be in 6 years. Use $y = y _ { 0 } e ^ { 0.042 t }$ and round to the nearest whole number.

Accepted Answer

A)  128 beavers 
B)  134 beavers 
C)  130 beavers 
D)  132 beavers 
A)  128 beavers 
B)  134 beavers 
C)  130 beavers 
D)  132 beavers

Question 5

Graph the function.
-$f(x)=6 \ln x$

Accepted Answer

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

Question 6

Determine whether the function is a one-to-one function.
-$\mathrm { f } = \{ ( 2,4 ) , ( - 2 , - 4 ) , ( - 1 , - 2 ) , ( 1,2 ) \}$

Accepted Answer

A)  not one-to-one 
B)  one-to-one 
A)  not one-to-one 
B)  one-to-one

Question 7

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 8

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines
the inverse function of the given function.
-

Accepted Answer

A) $\text { one-to-one; }$ 
  
B)  not one-to-one 
C)  one-to-one;   
 
D)  one-to-one;    
A) $\text { one-to-one; }$ 
  
B)  not one-to-one 
C)  one-to-one;   
 
D)  one-to-one;

Question 9

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 5 } \frac { x ^ { 5 } } { y ^ { 8 } }$

Accepted Answer

A)  $5 \log _ { 5 } x + 8 \log _ { 5 } y$ 
B)  $5 \log _ { 5 } x - 8 \log _ { 5 } y$ 
C)  $\frac { 5 } { 8 } \log _ { 5 } \frac { x } { y }$ 
D)  $8 \log _ { 5 } y - 5 \log _ { 5 } x$ 
A)  $5 \log _ { 5 } x + 8 \log _ { 5 } y$ 
B)  $5 \log _ { 5 } x - 8 \log _ { 5 } y$ 
C)  $\frac { 5 } { 8 } \log _ { 5 } \frac { x } { y }$ 
D)  $8 \log _ { 5 } y - 5 \log _ { 5 } x$

Question 10

Find the inverse of the one-to-one function.
-$f ( x ) = \sqrt [ 3 ] { x + 6 }$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x - 6$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 3 } + 36$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } ^ { 3 } - 6 }$ 
D)  $f ^ { - 1 } ( x ) = x ^ { 3 } - 6$ 
A)  $f ^ { - 1 } ( x ) = x - 6$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 3 } + 36$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } ^ { 3 } - 6 }$ 
D)  $f ^ { - 1 } ( x ) = x ^ { 3 } - 6$

Question 11

Solve the equation for x. Give an approximate solution accurate to four decimal places.
-$\log x = 1.8$

Accepted Answer

A)  $63.0957$ 
B)  $79.4328$ 
C)  $100.0000$ 
D)  $6.0496$ 
A)  $63.0957$ 
B)  $79.4328$ 
C)  $100.0000$ 
D)  $6.0496$

Question 12

Solve for x.
-$\log _ { 2 / 5 } x = 3$

Accepted Answer

A)  $3 ^ { 2 / 5 }$ 
B)  $\frac { 8 } { 5 }$ 
C)  $\frac { 8 } { 125 }$ 
D)  $\frac { 2 } { 5 }$ 
A)  $3 ^ { 2 / 5 }$ 
B)  $\frac { 8 } { 5 }$ 
C)  $\frac { 8 } { 125 }$ 
D)  $\frac { 2 } { 5 }$

Question 13

Solve the equation for x. Give an approximate solution accurate to four decimal places.
-$\ln x = 0.6$

Accepted Answer

A)  $2.2255$ 
B)  $1.8221$ 
C)  $2.0138$ 
D)  $3.9811$ 
A)  $2.2255$ 
B)  $1.8221$ 
C)  $2.0138$ 
D)  $3.9811$

Question 14

Solve the logarithmic equation for x. Give an exact solution
-$\log _ { 3 } ( x + 2 ) - \log _ { 3 } ( x - 4 ) = 3$

Accepted Answer

A)  $\frac { 3 } { 13 }$ 
B)  $\frac { 19 } { 4 }$ 
C)  21 
D)  $\frac { 55 } { 13 }$ 
A)  $\frac { 3 } { 13 }$ 
B)  $\frac { 19 } { 4 }$ 
C)  21 
D)  $\frac { 55 } { 13 }$

Question 15

The reliability of a new model of CD player can be described by the exponential function R(t) = 2.7-S1U1P1(1/3S1S1P0)S1U1P1tS1S1P0, where the
reliability R is the probability (as a decimal) that the CD player is still working t years after it is manufactured. Round the
answer to the nearest hundredth. Then write your answer as a percent.
-What is the probability that the CD player will still work 4 years after it is manufactured?

Accepted Answer

A)  $2 \%$ 
B)  $9 \%$ 
C)  $92 \%$ 
D)  $27 \%$ 
A)  $2 \%$ 
B)  $9 \%$ 
C)  $92 \%$ 
D)  $27 \%$

Question 16

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$\mathrm { f } = \{ ( - 5,10 ) , ( - 14 , - 1 ) , ( 19,16 ) \}$

Accepted Answer

A)  not one-to-one 
B)  $f ^ { - 1 } = \{ ( 10 , - 5 ) , ( - 1 , - 14 ) , ( 16,19 ) \}$ 
C)  $f ^ { - 1 } = \{ ( 10 , - 5 ) , ( 19 , - 14 ) , ( 16 , - 1 ) \}$ 
D)  $f ^ { - 1 } = \{ ( - 5 , - 1 ) , ( - 5 , - 14 ) , ( 16,19 ) \}$ 
A)  not one-to-one 
B)  $f ^ { - 1 } = \{ ( 10 , - 5 ) , ( - 1 , - 14 ) , ( 16,19 ) \}$ 
C)  $f ^ { - 1 } = \{ ( 10 , - 5 ) , ( 19 , - 14 ) , ( 16 , - 1 ) \}$ 
D)  $f ^ { - 1 } = \{ ( - 5 , - 1 ) , ( - 5 , - 14 ) , ( 16,19 ) \}$

Question 17

Write as a logarithmic equation.
-$7 ^ { 3 } = 343$

Accepted Answer

A)  $\log _ { 343 } ^ { 7 } = 3$ 
B)  $\log _ { 3 } ^ { 343 } = 7$ 
C)  $\log _ { 7 } ^ { 343 } = 3$ 
D)  $\log _ { 7 } ^ { 3 }= 343$ 
A)  $\log _ { 343 } ^ { 7 } = 3$ 
B)  $\log _ { 3 } ^ { 343 } = 7$ 
C)  $\log _ { 7 } ^ { 343 } = 3$ 
D)  $\log _ { 7 } ^ { 3 }= 343$

Question 18

Given the values of f and g, find the function value.
-$f ( 20 ) = 5 ; g ( 20 ) = 8 \quad$ Find $( f \cdot g ) ( 20 )$.

Accepted Answer

A)  4 
B)  40 
C)  $- 40$ 
D)  59 
A)  4 
B)  40 
C)  $- 40$ 
D)  59

Question 19

Solve the equation.
-$\log _ { 8 } x ^ { 2 } = \log _ { 8 } ( 3 x + 28 )$

Accepted Answer

A)  7 
B)  $\frac { 7 } { 8 }$ 
C)  $7 , - 4$ 
D)  $\varnothing$ 
A)  7 
B)  $\frac { 7 } { 8 }$ 
C)  $7 , - 4$ 
D)  $\varnothing$

Question 20

Use the power property to rewrite the expression.
-$\log _ { 7 } x ^ { 2 }$

Accepted Answer

A)  $2 \log _ { 7 } x ^ { 2 }$ 
B)  $7 \log x$ 
C)  $2 \log _ { 7 } x$ 
D)  $7 \log _ { 2 } x$ 
A)  $2 \log _ { 7 } x ^ { 2 }$ 
B)  $7 \log x$ 
C)  $2 \log _ { 7 } x$ 
D)  $7 \log _ { 2 } x$

Find the value of the logarithmic expression. - $\log _ { 2 } 8$

Solve the equation. - $\log _ { 7 } ( x + 2 ) - \log _ { 7 } x = 2$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { \mathrm { C } } \mathrm { m } + \log _ { \mathrm { C } } \mathrm { n }$

Solve. -The size of the beaver population at a national park increases at the rate of $4.2 \%$ per year. If the size of the current population is 101 , find how many beavers there should be in 6 years. Use $y = y _ { 0 } e ^ { 0.042 t }$ and round to the nearest whole number.

Graph the function. - $f(x)=6 \ln x$ $Graph the function. - f(x)=6 \ln x$

Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( 2,4 ) , ( - 2 , - 4 ) , ( - 1 , - 2 ) , ( 1,2 ) \}$

Graph the inverse of the function on the same set of axes. -

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. -

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 5 } \frac { x ^ { 5 } } { y ^ { 8 } }$

Find the inverse of the one-to-one function. - $f ( x ) = \sqrt [ 3 ] { x + 6 }$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log x = 1.8$

Solve for x. - $\log _ { 2 / 5 } x = 3$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\ln x = 0.6$

Solve the logarithmic equation for x. Give an exact solution - $\log _ { 3 } ( x + 2 ) - \log _ { 3 } ( x - 4 ) = 3$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $\mathrm { f } = \{ ( - 5,10 ) , ( - 14 , - 1 ) , ( 19,16 ) \}$

Write as a logarithmic equation. - $7 ^ { 3 } = 343$

Given the values of f and g, find the function value. - $f ( 20 ) = 5 ; g ( 20 ) = 8 \quad$ Find $( f \cdot g ) ( 20 )$ .

Solve the equation. - $\log _ { 8 } x ^ { 2 } = \log _ { 8 } ( 3 x + 28 )$

Use the power property to rewrite the expression. - $\log _ { 7 } x ^ { 2 }$

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

Find the value of the logarithmic expression. - log⁡28\log _ { 2 } 8log2​8

Solve the equation. - log⁡7(x+2)−log⁡7x=2\log _ { 7 } ( x + 2 ) - \log _ { 7 } x = 2log7​(x+2)−log7​x=2

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡Cm+log⁡Cn\log _ { \mathrm { C } } \mathrm { m } + \log _ { \mathrm { C } } \mathrm { n }logC​m+logC​n

Graph the function. - f(x)=6ln⁡xf(x)=6 \ln xf(x)=6lnx

Determine whether the function is a one-to-one function. - f={(2,4),(−2,−4),(−1,−2),(1,2)}\mathrm { f } = \{ ( 2,4 ) , ( - 2 , - 4 ) , ( - 1 , - 2 ) , ( 1,2 ) \}f={(2,4),(−2,−4),(−1,−2),(1,2)}