Question 1

Use a calculator to approximate the natural logarithm to four decimal places.
-$\ln 0.990$

Accepted Answer

A)  $- 0.0101$ 
B)  $0.0101$ 
C)  $- 0.0044$ 
D)  $0.0044$ 
A)  $- 0.0101$ 
B)  $0.0101$ 
C)  $- 0.0044$ 
D)  $0.0044$

Question 2

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
-$$h ( x ) = \frac { 1 } { x + 5 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x - 1 } ; g ( x ) = x + 5$ 
B)  $f ( x ) = x + 5 ; g ( x ) = \frac { 1 } { x }$ 
C)  $f ( x ) = \frac { 5 } { x } ; g ( x ) = x - 1$ 
D)  $f ( x ) = \frac { 1 } { x } ; g ( x ) = x + 5$ 
A)  $f ( x ) = \frac { 1 } { x - 1 } ; g ( x ) = x + 5$ 
B)  $f ( x ) = x + 5 ; g ( x ) = \frac { 1 } { x }$ 
C)  $f ( x ) = \frac { 5 } { x } ; g ( x ) = x - 1$ 
D)  $f ( x ) = \frac { 1 } { x } ; g ( x ) = x + 5$

Question 3

Graph the exponential function.
-$f(x)=\left(\frac{1}{5}\right)^{x}$

Accepted Answer

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

Question 4

Solve for x.
-$$\log _ { 3 } 9 = x$$

Accepted Answer

A)  $\{ 27 \}$ 
B)  $\{ 12 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ 27 \}$ 
B)  $\{ 12 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 3 \}$

Question 5

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
-$$h ( x ) = \left( 9 - 8 x ^ { 3 } \right) ^ { 2 }$$

Accepted Answer

A)  $f ( x ) = 9 - 8 x ^ { 3 } ; g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 8 x$ 
C)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 8 x ^ { 3 }$ 
D)  $f ( x ) = 9 - 8 x ^ { 2 } ; g ( x ) = x ^ { 3 }$ 
A)  $f ( x ) = 9 - 8 x ^ { 3 } ; g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 8 x$ 
C)  $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 8 x ^ { 3 }$ 
D)  $f ( x ) = 9 - 8 x ^ { 2 } ; g ( x ) = x ^ { 3 }$

Question 6

Solve.
-The formula $\mathrm { P } = 14.7 \mathrm { e } ^ { 0.21 \mathrm { x } }$ gives the average atmospheric pressure $\mathrm { P }$, in pounds per square inch, at an altitude $x$, in miles above sea level. Find the average atmospheric pressure of a mountain town that is $0.8$ miles above sea level.

Accepted Answer

A)  $14.5 \mathrm { psi }$ 
B)  $17.4 \mathrm { psi }$ 
C)  $- 13.9 \mathrm { psi }$ 
D)  $40.4 \mathrm { psi }$ 
A)  $14.5 \mathrm { psi }$ 
B)  $17.4 \mathrm { psi }$ 
C)  $- 13.9 \mathrm { psi }$ 
D)  $40.4 \mathrm { psi }$

Question 7

Solve the logarithmic equation. Give an exact solution.
-$\ln \sqrt [ 5 ] { \mathrm { e } } = \mathrm { x }$

Accepted Answer

A)  $\left\{ \mathrm { e } ^ { 1 / 2 } \right\}$ 
B)  $\left\{ \ln \frac { 1 } { 2 } \right\}$ 
C)  $\{ 2 \}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
A)  $\left\{ \mathrm { e } ^ { 1 / 2 } \right\}$ 
B)  $\left\{ \ln \frac { 1 } { 2 } \right\}$ 
C)  $\{ 2 \}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$

Question 8

For the given one-to-one function f, find the following.
-$$f ( x ) = x ^ { 3 } + 9$$
Find $f ( - 1 )$ and $f ^ { - 1 } ( 8 )$.

Accepted Answer

A)  $f ( - 1 ) = - 10 ; f ^ { - 1 } ( 8 ) = - 1$ 
B)  $f ( - 1 ) = 8 ; f ^ { - 1 } ( 8 ) = \frac { 1 } { 8 }$ 
C)  $f ( - 1 ) = 8 ; f ^ { - 1 } ( 8 ) = - 1$ 
D)  $f ( - 1 ) = - 1 ; f ^ { - 1 } ( 8 ) = 8$ 
A)  $f ( - 1 ) = - 10 ; f ^ { - 1 } ( 8 ) = - 1$ 
B)  $f ( - 1 ) = 8 ; f ^ { - 1 } ( 8 ) = \frac { 1 } { 8 }$ 
C)  $f ( - 1 ) = 8 ; f ^ { - 1 } ( 8 ) = - 1$ 
D)  $f ( - 1 ) = - 1 ; f ^ { - 1 } ( 8 ) = 8$

Question 9

Find the value of the logarithmic expression.
-$\log _ { 5 } 25$

Accepted Answer

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

Question 10

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 6 } \sqrt { 10 x }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 6 } 10 + \frac { 1 } { 2 } \log _ { 6 } x$ 
B)  $\log _ { 6 } 10 + \frac { 1 } { 2 } \log _ { 6 } x$ 
C)  $\log _ { 6 } \sqrt { 10 } + \log _ { 6 } \sqrt { x }$ 
D)  $\frac { 1 } { 2 } \log _ { 6 } 10 \mathrm { x }$ 
A)  $\frac { 1 } { 2 } \log _ { 6 } 10 + \frac { 1 } { 2 } \log _ { 6 } x$ 
B)  $\log _ { 6 } 10 + \frac { 1 } { 2 } \log _ { 6 } x$ 
C)  $\log _ { 6 } \sqrt { 10 } + \log _ { 6 } \sqrt { x }$ 
D)  $\frac { 1 } { 2 } \log _ { 6 } 10 \mathrm { x }$

Question 11

The reliability of a new model of CD player can be described by the exponential function R(t) = 2.7-(1/3)t, 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 5 years after it is manufactured?

Accepted Answer

A)  1% 
B)  94% 
C)  19% 
D)  7% 
A)  1% 
B)  94% 
C)  19% 
D)  7%

Question 12

Solve the equation.
-$$4 ( 11 - 3 x ) = 16$$

Accepted Answer

A)  $\{ - 3 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 4 \}$ 
A)  $\{ - 3 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 4 \}$

Question 13

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural half-life } & \text { horizontal }
\end{array}$$
-For a one-to-one function, we can find itsـــــــــــ function by switching the coordinates of the ordered pairs of the function.

Accepted Answer

A)  natural 
B)  inverse 
C)  composition 
D)  symmetric 
A)  natural 
B)  inverse 
C)  composition 
D)  symmetric

Question 14

Solve the logarithmic equation. Give an exact solution.
-$$\log _ { 7 } x + \log _ { 7 } 3 = 2$$

Accepted Answer

A)  $\left\{ \frac { 49 } { 3 } \right\}$ 
B)  $\left\{ \frac { 7 } { 3 } \right\}$ 
C)  $\{ 46 \}$ 
D)  $\left\{ \frac { 7 } { 6 } \right\}$ 
A)  $\left\{ \frac { 49 } { 3 } \right\}$ 
B)  $\left\{ \frac { 7 } { 3 } \right\}$ 
C)  $\{ 46 \}$ 
D)  $\left\{ \frac { 7 } { 6 } \right\}$

Question 15

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.
-$$f = \{ ( 0,0 ) , ( 1,5 ) , ( - 2,10 ) \}$$

Accepted Answer

A)  one-to-one; $\mathrm { f } ^ { - 1 } = \{ ( 0,0 ) , ( 5 , - 2 ) , ( 10,1 ) \}$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } = \left\{ ( 0,0 ) , \left( 1 , \frac { 1 } { 5 } \right) , \left( - 2 , \frac { 1 } { 10 } \right) \right\}$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } = \{ ( 0,0 ) , ( 5,1 ) , ( 10 , - 2 ) \}$ 
D)  not one-to-one 
A)  one-to-one; $\mathrm { f } ^ { - 1 } = \{ ( 0,0 ) , ( 5 , - 2 ) , ( 10,1 ) \}$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } = \left\{ ( 0,0 ) , \left( 1 , \frac { 1 } { 5 } \right) , \left( - 2 , \frac { 1 } { 10 } \right) \right\}$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } = \{ ( 0,0 ) , ( 5,1 ) , ( 10 , - 2 ) \}$ 
D)  not one-to-one

Question 16

Graph the function.
-$f ( x ) = 3 \ln x$

Accepted Answer

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

Question 17

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural half-life } & \text { horizontal }
\end{array}$$
-logarithms are logarithms to base e.

Accepted Answer

A)  Common 
B)  Natural 
C)  Exponential 
D)  Inverse 
A)  Common 
B)  Natural 
C)  Exponential 
D)  Inverse

Question 18

Solve the equation. Give an exact solution.
-$$e ^ { 4 x } = 7$$

Accepted Answer

A)  $\left\{ \frac { \ln 4 } { 7 } \right\}$ 
B)  $\left\{ \frac { \ln 7 } { 4 } \right\}$ 
C)  $\{ 4 \ln 7 \}$ 
D)  $\left\{ \frac { 7 } { 4 } \mathrm { e } \right\}$ 
A)  $\left\{ \frac { \ln 4 } { 7 } \right\}$ 
B)  $\left\{ \frac { \ln 7 } { 4 } \right\}$ 
C)  $\{ 4 \ln 7 \}$ 
D)  $\left\{ \frac { 7 } { 4 } \mathrm { e } \right\}$

Question 19

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Growth } \
\text { Rate per Year }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years, }
\end{array} & \begin{array}{l}
\text { Final Amount after } \
\text { x Years of Growth }
\end{array} \
\hline 26 & 64 \% & 16 &
\end{array}$

Accepted Answer

A)  64,562 
B)  78,472 
C)  346,964 
D)  71,199 
A)  64,562 
B)  78,472 
C)  346,964 
D)  71,199

Question 20

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

Accepted Answer

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

Use a calculator to approximate the natural logarithm to four decimal places. - $\ln 0.990$

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \frac { 1 } { x + 5 }$

Graph the exponential function. - $f(x)=\left(\frac{1}{5}\right)^{x}$ $Graph the exponential function. - f(x)=\left(\frac{1}{5}\right)^{x}$

Solve for x. - $\log _ { 3 } 9 = x$

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \left( 9 - 8 x ^ { 3 } \right) ^ { 2 }$

Solve the logarithmic equation. Give an exact solution. - $\ln \sqrt [ 5 ] { \mathrm { e } } = \mathrm { x }$

For the given one-to-one function f, find the following. - $f ( x ) = x ^ { 3 } + 9$ Find $f ( - 1 )$ and $f ^ { - 1 } ( 8 )$ .

Find the value of the logarithmic expression. - $\log _ { 5 } 25$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 6 } \sqrt { 10 x }$

Solve the equation. - $4 ( 11 - 3 x ) = 16$

Solve the logarithmic equation. Give an exact solution. - $\log _ { 7 } x + \log _ { 7 } 3 = 2$

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. - $f = \{ ( 0,0 ) , ( 1,5 ) , ( - 2,10 ) \}$

Graph the function. - $f ( x ) = 3 \ln x$ $Graph the function. - f ( x ) = 3 \ln x$

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal -logarithms are logarithms to base e.

Solve the equation. Give an exact solution. - $e ^ { 4 x } = 7$

Use the exponential growth formula to find the final amount. Round to the nearest whole. - Original Amount Growth Rate per Year Number of Years, Final Amount after x Years of Growth 26 64\% 16

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

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Exam 9: Exponential and Logarithmic Functions

Use a calculator to approximate the natural logarithm to four decimal places. - ln⁡0.990\ln 0.990ln0.990

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - h(x)=1x+5h ( x ) = \frac { 1 } { x + 5 }h(x)=x+51​

Graph the exponential function. - f(x)=(15)xf(x)=\left(\frac{1}{5}\right)^{x}f(x)=(51​)x

Solve for x. - log⁡39=x\log _ { 3 } 9 = xlog3​9=x

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - h(x)=(9−8x3)2h ( x ) = \left( 9 - 8 x ^ { 3 } \right) ^ { 2 }h(x)=(9−8x3)2

Solve the logarithmic equation. Give an exact solution. - ln⁡e5=x\ln \sqrt [ 5 ] { \mathrm { e } } = \mathrm { x }ln5e​=x

For the given one-to-one function f, find the following. - f(x)=x3+9f ( x ) = x ^ { 3 } + 9f(x)=x3+9 Find f(−1)f ( - 1 )f(−1) and f−1(8)f ^ { - 1 } ( 8 )f−1(8) .

Find the value of the logarithmic expression. - log⁡525\log _ { 5 } 25log5​25

Write the expression as sums or differences of multiples of logarithms. - log⁡610x\log _ { 6 } \sqrt { 10 x }log6​10x​

Solve the equation. - 4(11−3x)=164 ( 11 - 3 x ) = 164(11−3x)=16

Solve the logarithmic equation. Give an exact solution. - log⁡7x+log⁡73=2\log _ { 7 } x + \log _ { 7 } 3 = 2log7​x+log7​3=2

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. - f={(0,0),(1,5),(−2,10)}f = \{ ( 0,0 ) , ( 1,5 ) , ( - 2,10 ) \}f={(0,0),(1,5),(−2,10)}

Graph the function. - f(x)=3ln⁡xf ( x ) = 3 \ln xf(x)=3lnx