Question 1

Solve the exponential equation algebraically.Approximate the result to three decimal places. 
 $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Accepted Answer

A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 2.079$ 
C)  $\ln 8 \approx 4.079$ 
D)  $\ln 8 \approx 1.079$ 
E)  $\ln 8 \approx 0.079$ 
A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 2.079$ 
C)  $\ln 8 \approx 4.079$ 
D)  $\ln 8 \approx 1.079$ 
E)  $\ln 8 \approx 0.079$

Question 2

Select the correct graph for the given function $y = 7 e ^ { - x / 4 }$

Accepted Answer

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

Question 3

Assume that x, y and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } x ^ { 6 } y ^ { 4 }$ in terms of the logarithms of x and y.

Accepted Answer

A)  $6 \log _ { c } x + 4 \log _ { c } y$ 
B)  $24 \log _ { c } x + y$ 
C)  $6 \log _ { c } x + 6 \log _ { c } y$ 
D)  $24 \log _ { c } x + 4 \log _ { c } y$ 
E)  $6 \log _ { c } x + 24 \log _ { c } y$ 
A)  $6 \log _ { c } x + 4 \log _ { c } y$ 
B)  $24 \log _ { c } x + y$ 
C)  $6 \log _ { c } x + 6 \log _ { c } y$ 
D)  $24 \log _ { c } x + 4 \log _ { c } y$ 
E)  $6 \log _ { c } x + 24 \log _ { c } y$

Question 4

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.)  $r = 0.0315$

Accepted Answer

A) 21.00 yr 
B) 20.00 yr 
C) 34.88 yr 
D) 24.00 yr 
E) 23.00 yr 
A) 21.00 yr 
B) 20.00 yr 
C) 34.88 yr 
D) 24.00 yr 
E) 23.00 yr

Question 5

Condense the expression to the logarithm of a single quantity. 
Log2 10 + log2 x

Accepted Answer

A) log2 (10 - x) 
B)  $\ln _ { 2 } \frac { 10 } { x }$ 
C) log2 (10 + x) 
D) log2 10x 
E) log2 10x 
A) log2 (10 - x) 
B)  $\ln _ { 2 } \frac { 10 } { x }$ 
C) log2 (10 + x) 
D) log2 10x 
E) log2 10x

Question 6

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.

F(x) = log4 x

Accepted Answer

A) f(x) = log x + log 4 = ln x + ln 4   
B)  $f ( x ) = \frac { \log 4 } { \log x } = \frac { \ln 4 } { \ln x }$   
C)  $f ( x ) = \log \frac { x } { 4 } = \ln \frac { x } { 4 }$   
D)  $f ( x ) = \log \frac { 4 } { x } = \ln \frac { 4 } { x }$   
E)  $f ( x ) = \frac { \log x } { \log 4 } = \frac { \ln x } { \ln 4 }$   
A) f(x) = log x + log 4 = ln x + ln 4   
B)  $f ( x ) = \frac { \log 4 } { \log x } = \frac { \ln 4 } { \ln x }$   
C)  $f ( x ) = \log \frac { x } { 4 } = \ln \frac { x } { 4 }$   
D)  $f ( x ) = \log \frac { 4 } { x } = \ln \frac { 4 } { x }$   
E)  $f ( x ) = \frac { \log x } { \log 4 } = \frac { \ln x } { \ln 4 }$

Question 7

Write the exponential equation in logarithmic form. $10 ^ { - 3 } = 0.00100$

Accepted Answer

A)  $\log 3 = 0.00100$ 
B)  $\log 0.00100 = - \frac { 1 } { 3 }$ 
C)  $\log 0.00100 = - 3$ 
D)  $\log 0.00100 = \frac { 1 } { 3 }$ 
E)  $\log 0.00100 = 3$ 
A)  $\log 3 = 0.00100$ 
B)  $\log 0.00100 = - \frac { 1 } { 3 }$ 
C)  $\log 0.00100 = - 3$ 
D)  $\log 0.00100 = \frac { 1 } { 3 }$ 
E)  $\log 0.00100 = 3$

Question 8

Solve the equation.Round to 3 decimal places. ​
5x = 8
​

Accepted Answer

A) x = 1.415 
B) x = 2.292 
C) x = 6.724 
D) x = 2.526 
E) x = 1.292 
A) x = 1.415 
B) x = 2.292 
C) x = 6.724 
D) x = 2.526 
E) x = 1.292

Question 9

Select the graph of the exponential function.  $f ( x ) = 4 ^ { x + 1 } - 6$

Accepted Answer

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

Question 10

Use a calculator to find a value for $\ln ( 30.9 )$ to four decimal places.

Accepted Answer

A) -3.4308 
B) 3.4308 
C) -1.49 
D) 1.49 
E) 5.7333 
A) -3.4308 
B) 3.4308 
C) -1.49 
D) 1.49 
E) 5.7333

Question 11

Solve the exponential equation algebraically.Approximate the result to three decimal places. 
 $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Accepted Answer

A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 1.079$ 
C)  $\ln 8 \approx 2.079$ 
D)  $\ln 8 \approx 0.079$ 
E)  $\ln 8 \approx 4.079$ 
A)  $\ln 8 \approx 3.079$ 
B)  $\ln 8 \approx 1.079$ 
C)  $\ln 8 \approx 2.079$ 
D)  $\ln 8 \approx 0.079$ 
E)  $\ln 8 \approx 4.079$

Question 12

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.  $\ln 2 x = 3$

Accepted Answer

A)  $\frac { e ^ { 3 } } { 2 } \approx 8.043$ 
B)  $\frac { e ^ { 3 } } { 2 } \approx 10.043$ 
C)  $\frac { e ^ { 3 } } { 2 } \approx 12.043$ 
D)  $\frac { e ^ { 3 } } { 2 } \approx 11.043$ 
E)  $\frac { e ^ { 3 } } { 2 } \approx 13.043$ 
A)  $\frac { e ^ { 3 } } { 2 } \approx 8.043$ 
B)  $\frac { e ^ { 3 } } { 2 } \approx 10.043$ 
C)  $\frac { e ^ { 3 } } { 2 } \approx 12.043$ 
D)  $\frac { e ^ { 3 } } { 2 } \approx 11.043$ 
E)  $\frac { e ^ { 3 } } { 2 } \approx 13.043$

Question 13

Evaluate the function $f ( x ) = 400 ( 1.005 ) ^ { x }$ at $x = 240$ .Round to 3 decimal places.

Accepted Answer

A) 1,324.082 
B) 1,764.558 
C) 404.010 
D) 96,480.000 
E) 3.310 
A) 1,324.082 
B) 1,764.558 
C) 404.010 
D) 96,480.000 
E) 3.310

Question 14

Select the graph of the function.  $f ( x ) = \log ( x + 5 )$

Accepted Answer

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

Question 15

Find the intensity I of an earthquake measuring R on the Richter scale $\text { (let } I _ { 0 } = 1 \text { ) }$ . 
Costa Rica in 2009, $R = 5.70$

Accepted Answer

A)  $10 ^ { 5.70 } \approx 503,187$ 
B)  $10 ^ { 5.70 } \approx 501,187$ 
C)  $10 ^ { 5.70 } \approx 506,187$ 
D)  $10 ^ { 5.70 } \approx 496,187$ 
E)  $10 ^ { 5.70 } \approx 499,187$ 
A)  $10 ^ { 5.70 } \approx 503,187$ 
B)  $10 ^ { 5.70 } \approx 501,187$ 
C)  $10 ^ { 5.70 } \approx 506,187$ 
D)  $10 ^ { 5.70 } \approx 496,187$ 
E)  $10 ^ { 5.70 } \approx 499,187$

Question 16

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x - 5 = 0$

Accepted Answer

A)  $e ^ { 5 } \approx 151.413$ 
B)  $e ^ { 5 } \approx 146.413$ 
C)  $e ^ { 5 } \approx 148.413$ 
D)  $e ^ { 5 } \approx 149.413$ 
E)  $e ^ { 5 } \approx 150.413$ 
A)  $e ^ { 5 } \approx 151.413$ 
B)  $e ^ { 5 } \approx 146.413$ 
C)  $e ^ { 5 } \approx 148.413$ 
D)  $e ^ { 5 } \approx 149.413$ 
E)  $e ^ { 5 } \approx 150.413$

Question 17

Select the graph of the exponential function.  $y = 1.02 ^ { - 2 x }$

Accepted Answer

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

Question 18

Condense the expression to the logarithm of a single quantity. 
Log x - 3log(x + 1)

Accepted Answer

A) 3log(x(x + 1)) 
B)  $3 \log \frac { x } { ( x + 1 ) }$ 
C)  $\log \frac { x } { ( x + 1 ) ^ { 3 } }$ 
D) log(x(x + 1)3) 
E)  $\frac { 1 } { 3 } \log \frac { x } { ( x + 1 ) }$ 
A) 3log(x(x + 1)) 
B)  $3 \log \frac { x } { ( x + 1 ) }$ 
C)  $\log \frac { x } { ( x + 1 ) ^ { 3 } }$ 
D) log(x(x + 1)3) 
E)  $\frac { 1 } { 3 } \log \frac { x } { ( x + 1 ) }$

Question 19

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.  $f ( x ) = e ^ { 5 x }$

Accepted Answer

A) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & 0.007 & - 1.000 & 148.413 & 22,026.466 \
\hline
\end{array}$ 
B) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & 0.007 & 1.000 & - 148.413 & 22,026.466 \
\hline
\end{array}$ 
C) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & 0.007 & 1.000 & 148.413 & 22,026.466 \
\hline
\end{array}$ 
D) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & - 0.007 & 1.000 & 148.413 & 22,026.466 \
\hline
\end{array}$ 
E) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & - 0.007 & - 1.000 & - 148.413 & - 22,026.466 \
\hline
\end{array}$ 
A) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & 0.007 & - 1.000 & 148.413 & 22,026.466 \
\hline
\end{array}$ 
B) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & 0.007 & 1.000 & - 148.413 & 22,026.466 \
\hline
\end{array}$ 
C) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & 0.007 & 1.000 & 148.413 & 22,026.466 \
\hline
\end{array}$ 
D) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & - 0.007 & 1.000 & 148.413 & 22,026.466 \
\hline
\end{array}$ 
E) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 0.000 & - 0.007 & - 1.000 & - 148.413 & - 22,026.466 \
\hline
\end{array}$

Question 20

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $6 ^ { - 5 x } = 0.50$

Accepted Answer

A)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.072$ 
B)  $\frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.517$ 
C)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.387$ 
D)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.077$ 
E)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx - 0.077$ 
A)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.072$ 
B)  $\frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.517$ 
C)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.387$ 
D)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.077$ 
E)  $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx - 0.077$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Select the correct graph for the given function $y = 7 e ^ { - x / 4 }$

Assume that x, y and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } x ^ { 6 } y ^ { 4 }$ in terms of the logarithms of x and y.

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) $r = 0.0315$

Condense the expression to the logarithm of a single quantity. Log₂ 10 + log₂ x

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio. F(x) = log₄ x

Write the exponential equation in logarithmic form. $10 ^ { - 3 } = 0.00100$

Solve the equation.Round to 3 decimal places. 5^x = 8

Select the graph of the exponential function. $f ( x ) = 4 ^ { x + 1 } - 6$

Use a calculator to find a value for $\ln ( 30.9 )$ to four decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln 2 x = 3$

Evaluate the function $f ( x ) = 400 ( 1.005 ) ^ { x }$ at $x = 240$ .Round to 3 decimal places.

Select the graph of the function. $f ( x ) = \log ( x + 5 )$

Find the intensity I of an earthquake measuring R on the Richter scale $\text { (let } I _ { 0 } = 1 \text { ) }$ . Costa Rica in 2009, $R = 5.70$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x - 5 = 0$

Select the graph of the exponential function. $y = 1.02 ^ { - 2 x }$

Condense the expression to the logarithm of a single quantity. Log x - 3log(x + 1)

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. $f ( x ) = e ^ { 5 x }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { - 5 x } = 0.50$

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 3: Exponential and Logarithmic Functions

Solve the exponential equation algebraically.Approximate the result to three decimal places. e2x−7ex−8=0e ^ { 2 x } - 7 e ^ { x } - 8 = 0e2x−7ex−8=0

Select the correct graph for the given function y=7e−x/4y = 7 e ^ { - x / 4 }y=7e−x/4

Assume that x, y and c are positive numbers.Use the properties of logarithms to write the expression log⁡cx6y4\log _ { c } x ^ { 6 } y ^ { 4 }logc​x6y4 in terms of the logarithms of x and y.

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) r=0.0315r = 0.0315r=0.0315

Condense the expression to the logarithm of a single quantity. Log2 10 + log2 x

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio. F(x) = log4 x

Write the exponential equation in logarithmic form. 10−3=0.0010010 ^ { - 3 } = 0.0010010−3=0.00100

Solve the equation.Round to 3 decimal places. ​ 5x = 8 ​

Select the graph of the exponential function. f(x)=4x+1−6f ( x ) = 4 ^ { x + 1 } - 6f(x)=4x+1−6

Use a calculator to find a value for ln⁡(30.9)\ln ( 30.9 )ln(30.9) to four decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places. e2x−7ex−8=0e ^ { 2 x } - 7 e ^ { x } - 8 = 0e2x−7ex−8=0

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ln⁡2x=3\ln 2 x = 3ln2x=3

Evaluate the function f(x)=400(1.005)xf ( x ) = 400 ( 1.005 ) ^ { x }f(x)=400(1.005)x at x=240x = 240x=240 .Round to 3 decimal places.

Select the graph of the function. f(x)=log⁡(x+5)f ( x ) = \log ( x + 5 )f(x)=log(x+5)

Find the intensity I of an earthquake measuring R on the Richter scale (let I0=1 ) \text { (let } I _ { 0 } = 1 \text { ) } (let I0​=1 ) . Costa Rica in 2009, R=5.70R = 5.70R=5.70

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ln⁡x−5=0\ln x - 5 = 0lnx−5=0

Select the graph of the exponential function. y=1.02−2xy = 1.02 ^ { - 2 x }y=1.02−2x

Condense the expression to the logarithm of a single quantity. Log x - 3log(x + 1)

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. f(x)=e5xf ( x ) = e ^ { 5 x }f(x)=e5x

Solve the exponential equation algebraically.Approximate the result to three decimal places. 6−5x=0.506 ^ { - 5 x } = 0.506−5x=0.50

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Select the correct graph for the given function $y = 7 e ^ { - x / 4 }$

Assume that x, y and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } x ^ { 6 } y ^ { 4 }$ in terms of the logarithms of x and y.

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) $r = 0.0315$

Condense the expression to the logarithm of a single quantity. Log₂ 10 + log₂ x

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio. F(x) = log₄ x

Write the exponential equation in logarithmic form. $10 ^ { - 3 } = 0.00100$

Solve the equation.Round to 3 decimal places. 5^x = 8

Select the graph of the exponential function. $f ( x ) = 4 ^ { x + 1 } - 6$

Use a calculator to find a value for $\ln ( 30.9 )$ to four decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln 2 x = 3$

Evaluate the function $f ( x ) = 400 ( 1.005 ) ^ { x }$ at $x = 240$ .Round to 3 decimal places.

Select the graph of the function. $f ( x ) = \log ( x + 5 )$

Find the intensity I of an earthquake measuring R on the Richter scale $\text { (let } I _ { 0 } = 1 \text { ) }$ . Costa Rica in 2009, $R = 5.70$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x - 5 = 0$

Select the graph of the exponential function. $y = 1.02 ^ { - 2 x }$

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. $f ( x ) = e ^ { 5 x }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { - 5 x } = 0.50$