Question 1

Write as an exponential equation.
-$\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 2 } } = - 2$

Accepted Answer

A)  $\left( \frac { 1 } { \mathrm { e } ^ { 2 } } \right) ^ { - 2 } = \mathrm { e }$ 
B)  $e ^ { - 2 } = \frac { 1 } { e ^ { 2 } }$ 
C)  $- 2 ^ { e } = \frac { 1 } { \mathrm { e } ^ { 2 } }$ 
D)  $\left( \frac { 1 } { \mathrm { e } ^ { 2 } } \right) ^ { \mathrm { e } } = - 2$ 
A)  $\left( \frac { 1 } { \mathrm { e } ^ { 2 } } \right) ^ { - 2 } = \mathrm { e }$ 
B)  $e ^ { - 2 } = \frac { 1 } { e ^ { 2 } }$ 
C)  $- 2 ^ { e } = \frac { 1 } { \mathrm { e } ^ { 2 } }$ 
D)  $\left( \frac { 1 } { \mathrm { e } ^ { 2 } } \right) ^ { \mathrm { e } } = - 2$

Question 2

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

Accepted Answer

A)  $\log _ { 2 b } ( x + y )$ 
B)  $\log _ { 2 b } x y$ 
C)  $\log _ { b } ( x + y )$ 
D)  $\log _ { b } x y$ 
A)  $\log _ { 2 b } ( x + y )$ 
B)  $\log _ { 2 b } x y$ 
C)  $\log _ { b } ( x + y )$ 
D)  $\log _ { b } x y$

Question 3

Graph the function and its inverse on the same set of axes.
-$f(x)=2 x-4$

Accepted Answer

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

Question 4

Use a calculator to approximate the logarithm to four decimal places.
-$\log 3080$

Accepted Answer

A)  $3.4900$ 
B)  $3.4886$ 
C)  $8.0327$ 
D)  $3.4871$ 
A)  $3.4900$ 
B)  $3.4886$ 
C)  $8.0327$ 
D)  $3.4871$

Question 5

Solve.
-Find out how long it takes a $\$ 3000$ investment to double if it is invested at $8 \%$ compounded quarterly. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$.

Accepted Answer

A)  $9.2$ years 
B)  $8.6$ years 
C)  9 years 
D)  $8.8$ years 
A)  $9.2$ years 
B)  $8.6$ years 
C)  9 years 
D)  $8.8$ years

Question 6

Solve for x.
-$\log _ { 9 } x = 1$

Accepted Answer

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

Question 7

Solve the equation.
-$9 ^ { x } = 27$

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 3 } { 2 }$ 
A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 3 } { 2 }$

Question 8

Use the properties of logarithms to write the expression as a single logarithm.
-$\log _ { 3 } 7 + \log _ { 3 } 11$

Accepted Answer

A)  $\log _ { 3 } 77$ 
B)  $\log _ { 3 } 18$ 
C)  $\log _ { 6 } 18$ 
D)  $\log _ { 6 } 77$ 
A)  $\log _ { 3 } 77$ 
B)  $\log _ { 3 } 18$ 
C)  $\log _ { 6 } 18$ 
D)  $\log _ { 6 } 77$

Question 9

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 5 } \frac { x + 6 } { x ^ { 3 } }$

Accepted Answer

A)  $\log _ { 5 } ( x + 6 ) - 3 \log _ { 5 } x$ 
B)  $3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )$ 
C)  $\log _ { 5 } ( x + 6 ) + 3 \log _ { 5 } x$ 
D)  $\log _ { 5 } ( x + 6 ) - \log _ { 5 } x$ 
A)  $\log _ { 5 } ( x + 6 ) - 3 \log _ { 5 } x$ 
B)  $3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )$ 
C)  $\log _ { 5 } ( x + 6 ) + 3 \log _ { 5 } x$ 
D)  $\log _ { 5 } ( x + 6 ) - \log _ { 5 } x$

Question 10

For the given functions f and g, find the composition.
-$f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quad$ Find $( f \circ g ) ( 4 )$

Accepted Answer

A)  60 
B)  0 
C)  $4 \sqrt { 3 }$ 
D)  34 
A)  60 
B)  0 
C)  $4 \sqrt { 3 }$ 
D)  34

Question 11

Write as an exponential equation.
-$\log _ { 10 } 0.00001 = - 5$

Accepted Answer

A)  $- 5 ^ { 10 } = 0.00001$ 
B)  $0.00001 ^ { 5 } = 10$ 
C)  $10 ^ { 5 } = 0.00001$ 
D)  $10 ^ { - 5 } = 0.00001$ 
A)  $- 5 ^ { 10 } = 0.00001$ 
B)  $0.00001 ^ { 5 } = 10$ 
C)  $10 ^ { 5 } = 0.00001$ 
D)  $10 ^ { - 5 } = 0.00001$

Question 12

Solve the equation.
-$\log _ { 12 } \left( x ^ { 2 } - x \right) = 1$

Accepted Answer

A)  $- 3,4$ 
B)  1,12 
C)  $- 3 , - 4$ 
D)  3,4 
A)  $- 3,4$ 
B)  1,12 
C)  $- 3 , - 4$ 
D)  3,4

Question 13

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

Accepted Answer

A)  $\frac { 1 } { 25 }$ 
B)  3 
C)  $\frac { 1 } { 32 }$ 
D)  $- 10$ 
A)  $\frac { 1 } { 25 }$ 
B)  3 
C)  $\frac { 1 } { 32 }$ 
D)  $- 10$

Question 14

$\log _ { 3 } 9 + \log _ { 3 } 27 = 5$

Accepted Answer

A) True 
 B)False

Question 15

Solve the equation.
-$\log _ { 3 } x = 4$

Accepted Answer

A)  12 
B)  64 
C)  $1.26$ 
D)  81 
A)  12 
B)  64 
C)  $1.26$ 
D)  81

Question 16

Use the following approximations to find the approximate value of the logarithmic expression: 
$\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$
$\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$
-$\log _ { b } 160$

Accepted Answer

A)  $1.17$ 
B)  28 
C)  $2.2$ 
D)  160 
A)  $1.17$ 
B)  28 
C)  $2.2$ 
D)  160

Question 17

Graph the function and its inverse on the same set of axes.
-$y = \log _ { 2 } x ; y = 2 ^ { x }$

Accepted Answer

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

Question 18

Solve.
-The amount of a radioactive substance present, in grams, at time $t$ in months is given by the formula $y = 8000 ( 3 ) ^ { - 0.3 t }$. Find the number of grams present in 4 years. If necessary, round to three decimal places.

Accepted Answer

A)  $0.001 \mathrm {~g}$ 
B)  $2140.644 \mathrm {~g}$ 
C)  $214.064 \mathrm {~g}$ 
D)  $0.000 \mathrm {~g}$ 
A)  $0.001 \mathrm {~g}$ 
B)  $2140.644 \mathrm {~g}$ 
C)  $214.064 \mathrm {~g}$ 
D)  $0.000 \mathrm {~g}$

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

Graph the exponential function.
-$f(x)=2^{x-1}$

Accepted Answer

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

Write as an exponential equation. - $\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 2 } } = - 2$

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

Graph the function and its inverse on the same set of axes. - $f(x)=2 x-4$

Use a calculator to approximate the logarithm to four decimal places. - $\log 3080$

Solve. -Find out how long it takes a $\$ 3000$ investment to double if it is invested at $8 \%$ compounded quarterly. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

Solve for x. - $\log _ { 9 } x = 1$

Solve the equation. - $9 ^ { x } = 27$

Use the properties of logarithms to write the expression as a single logarithm. - $\log _ { 3 } 7 + \log _ { 3 } 11$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 5 } \frac { x + 6 } { x ^ { 3 } }$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quad$ Find $( f \circ g ) ( 4 )$

Write as an exponential equation. - $\log _ { 10 } 0.00001 = - 5$

Solve the equation. - $\log _ { 12 } \left( x ^ { 2 } - x \right) = 1$

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

$\log _ { 3 } 9 + \log _ { 3 } 27 = 5$

Solve the equation. - $\log _ { 3 } x = 4$

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$ $\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$ - $\log _ { b } 160$

Graph the function and its inverse on the same set of axes. - $y = \log _ { 2 } x ; y = 2 ^ { x }$ $Graph the function and its inverse on the same set of axes. - y = \log _ { 2 } x ; y = 2 ^ { x }$

Solve. -The amount of a radioactive substance present, in grams, at time $t$ in months is given by the formula $y = 8000 ( 3 ) ^ { - 0.3 t }$ . Find the number of grams present in 4 years. If necessary, round to three decimal places.

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

Graph the exponential function. - $f(x)=2^{x-1}$ $Graph the exponential function. - f(x)=2^{x-1}$

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

Write as an exponential equation. - log⁡e1e2=−2\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 2 } } = - 2loge​e21​=−2

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡bx+log⁡by\log _ { b } x + \log _ { b } ylogb​x+logb​y

Graph the function and its inverse on the same set of axes. - f(x)=2x−4f(x)=2 x-4f(x)=2x−4

Use a calculator to approximate the logarithm to four decimal places. - log⁡3080\log 3080log3080

Solve. -Find out how long it takes a $3000\$ 3000$3000 investment to double if it is invested at 8%8 \%8% compounded quarterly. Round to the nearest tenth of a year. Use the formula A=P(1+rn)ntA = P \left( 1 + \frac { r } { n } \right) ^ { n t }A=P(1+nr​)nt .

Solve for x. - log⁡9x=1\log _ { 9 } x = 1log9​x=1

Solve the equation. - 9x=279 ^ { x } = 279x=27

Use the properties of logarithms to write the expression as a single logarithm. - log⁡37+log⁡311\log _ { 3 } 7 + \log _ { 3 } 11log3​7+log3​11

Write the expression as sums or differences of multiples of logarithms. - log⁡5x+6x3\log _ { 5 } \frac { x + 6 } { x ^ { 3 } }log5​x3x+6​

For the given functions f and g, find the composition. - f(x)=x2+4x;g(x)=x+2f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quadf(x)=x2+4x;g(x)=x+2 Find (f∘g)(4)( f \circ g ) ( 4 )(f∘g)(4)

Write as an exponential equation. - log⁡100.00001=−5\log _ { 10 } 0.00001 = - 5log10​0.00001=−5

Solve the equation. - log⁡12(x2−x)=1\log _ { 12 } \left( x ^ { 2 } - x \right) = 1log12​(x2−x)=1

Solve for x. - log⁡5x=−2\log _ { 5 } x = - 2log5​x=−2

log⁡39+log⁡327=5\log _ { 3 } 9 + \log _ { 3 } 27 = 5log3​9+log3​27=5

Solve the equation. - log⁡3x=4\log _ { 3 } x = 4log3​x=4

Graph the function and its inverse on the same set of axes. - y=log⁡2x;y=2xy = \log _ { 2 } x ; y = 2 ^ { x }y=log2​x;y=2x

Solve. -The amount of a radioactive substance present, in grams, at time ttt in months is given by the formula y=8000(3)−0.3ty = 8000 ( 3 ) ^ { - 0.3 t }y=8000(3)−0.3t . Find the number of grams present in 4 years. If necessary, round to three decimal places.

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

Graph the exponential function. - f(x)=2x−1f(x)=2^{x-1}f(x)=2x−1

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

Write as an exponential equation. - $\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 2 } } = - 2$

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

Graph the function and its inverse on the same set of axes. - $f(x)=2 x-4$

Use a calculator to approximate the logarithm to four decimal places. - $\log 3080$

Solve. -Find out how long it takes a $\$ 3000$ investment to double if it is invested at $8 \%$ compounded quarterly. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

Solve for x. - $\log _ { 9 } x = 1$

Solve the equation. - $9 ^ { x } = 27$

Use the properties of logarithms to write the expression as a single logarithm. - $\log _ { 3 } 7 + \log _ { 3 } 11$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 5 } \frac { x + 6 } { x ^ { 3 } }$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quad$ Find $( f \circ g ) ( 4 )$

Write as an exponential equation. - $\log _ { 10 } 0.00001 = - 5$

Solve the equation. - $\log _ { 12 } \left( x ^ { 2 } - x \right) = 1$

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

$\log _ { 3 } 9 + \log _ { 3 } 27 = 5$

Solve the equation. - $\log _ { 3 } x = 4$

Graph the function and its inverse on the same set of axes. - $y = \log _ { 2 } x ; y = 2 ^ { x }$ $Graph the function and its inverse on the same set of axes. - y = \log _ { 2 } x ; y = 2 ^ { x }$

Solve. -The amount of a radioactive substance present, in grams, at time $t$ in months is given by the formula $y = 8000 ( 3 ) ^ { - 0.3 t }$ . Find the number of grams present in 4 years. If necessary, round to three decimal places.

Graph the exponential function. - $f(x)=2^{x-1}$ $Graph the exponential function. - f(x)=2^{x-1}$