Question 1

Use the One-to-One Property to solve the equation for x.  $\left( \frac { 1 } { 2 } \right) ^ { x } = 4$

Accepted Answer

A)  $x = 3$ 
B)  $x = - 2$ 
C)  $x = 2$ 
D)  $x = - 3$ 
E)  $x = 4$ 
A)  $x = 3$ 
B)  $x = - 2$ 
C)  $x = 2$ 
D)  $x = - 3$ 
E)  $x = 4$

Question 2

Select the graph of the function.  $f ( x ) = 2 ^ { x - 1 }$

Accepted Answer

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

Question 3

Evaluate the function $f ( x ) = \frac { 1 } { 4 } \ln x$ at $x = 4.461$ .Round to 3 decimal places.(You may use your calculator.)

Accepted Answer

A) undefined 
B) 1.106 
C) 0.374 
D) 0.861 
E) -0.347 
A) undefined 
B) 1.106 
C) 0.374 
D) 0.861 
E) -0.347

Question 4

Graph the exponential function.  $f ( x ) = 4 ^ { x } + 1$

Accepted Answer

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

Question 5

Assume that x, y, and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } 5 x y$ in terms of the logarithms of x and y.

Accepted Answer

A)  $\log _ { c } 5 + \log _ { c } x y$ 
B)  $\log _ { c } 5 + \log _ { c } x + \log _ { c } y$ 
C)  $\log _ { c } 5 + \log _ { c } x$ 
D)  $\log _ { c } 5 + \log _ { 5 } x + \log _ { 5 } y$ 
E)  $\log _ { c } 5 + \log _ { c } y$ 
A)  $\log _ { c } 5 + \log _ { c } x y$ 
B)  $\log _ { c } 5 + \log _ { c } x + \log _ { c } y$ 
C)  $\log _ { c } 5 + \log _ { c } x$ 
D)  $\log _ { c } 5 + \log _ { 5 } x + \log _ { 5 } y$ 
E)  $\log _ { c } 5 + \log _ { c } y$

Question 6

Solve the equation $\log ( 1 - x ) = \log ( 10 )$ for x using the One-to-One Property.

Accepted Answer

A) 11 
B) -9 
C) -11 
D) 0 
E) The equation has no solution. 
A) 11 
B) -9 
C) -11 
D) 0 
E) The equation has no solution.

Question 7

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $3 ^ { 8 x } = 2400$

Accepted Answer

A)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.018$ 
B)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.886$ 
C)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.089$ 
D)  $\frac { \ln 2400 } { 8 \ln 3 } \approx - 0.886$ 
E)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 1.248$ 
A)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.018$ 
B)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.886$ 
C)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.089$ 
D)  $\frac { \ln 2400 } { 8 \ln 3 } \approx - 0.886$ 
E)  $\frac { \ln 2400 } { 8 \ln 3 } \approx 1.248$

Question 8

Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is 14C is constant.The amount of 14C in an object made from harvested plants, like paper, will decline exponentially according to the equation $A = A _ { 0 } e ^ { - 0.0001213 t }$ , where A represents the amount of 14C in the object, Ao represents the amount of 14C in living organisms, and t is the time in years since the plant was harvested.If an archeological artifact has 35% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.

Accepted Answer

A) 5715 years 
B) 29,310 years 
C) 93 years 
D) 8655 years 
E) 15,427 years 
A) 5715 years 
B) 29,310 years 
C) 93 years 
D) 8655 years 
E) 15,427 years

Question 9

Select the graph of the exponential function.  $s ( t ) = 3 e ^ { 0.13 t }$

Accepted Answer

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

Question 10

Match the graph with its exponential function.

Accepted Answer

A)  $y = 5 ^ { - x } - 3$ 
B)  $y = - 5 ^ { x } + 3$ 
C)  $y = 5 ^ { x } + 3$ 
D)  $y = 5 ^ { x } - 3$ 
E)  $y = - 5 ^ { x } - 3$ 
A)  $y = 5 ^ { - x } - 3$ 
B)  $y = - 5 ^ { x } + 3$ 
C)  $y = 5 ^ { x } + 3$ 
D)  $y = 5 ^ { x } - 3$ 
E)  $y = - 5 ^ { x } - 3$

Question 11

Condense the expression to the logarithm of a single quantity. 
Ln 8 + ln x

Accepted Answer

A) ln x8 
B) ln 8x 
C)  $\ln \frac { 8 } { x }$ 
D) ln 8x 
E) ln 8 × ln x 
A) ln x8 
B) ln 8x 
C)  $\ln \frac { 8 } { x }$ 
D) ln 8x 
E) ln 8 × ln x

Question 12

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.  $\log x = 4$

Accepted Answer

A) 1,000 
B) 1,000,000 
C) 10,000 
D) 100,000 
E) 100 
A) 1,000 
B) 1,000,000 
C) 10,000 
D) 100,000 
E) 100

Question 13

Select the correct graph for the given function  $y = \frac { 6 } { 1 + e ^ { - 2 x } }$

Accepted Answer

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

Question 14

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$$

Accepted Answer

A) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f(x)& 25.00 & - 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$ 
B) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & - 1.00 & 0.20 & 0.04 \
& & & & & \
\hline
\end{array}$ 
C) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & - 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
& & & & & \
\hline
\end{array}$ 
D) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$ 
E) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 25.00 & 5.00 & 1.00 & - 0.20 & - 0.04 \
& & & & & \
\hline
\end{array}$ 
A) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f(x)& 25.00 & - 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$ 
B) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & - 1.00 & 0.20 & 0.04 \
& & & & & \
\hline
\end{array}$ 
C) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & - 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
& & & & & \
\hline
\end{array}$ 
D) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$ 
E) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 25.00 & 5.00 & 1.00 & - 0.20 & - 0.04 \
& & & & & \
\hline
\end{array}$

Question 15

Condense the expression to the logarithm of a single quantity.  $2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]$

Accepted Answer

A)  $\ln \left( \frac { x ^ { 3 } } { ( x - 8 ) ( x + 8 ) } \right) ^ { 2 }$ 
B)  $\ln \left( \frac { x ^ { 3 } ( x + 8 ) } { ( x - 8 ) } \right) ^ { 2 }$ 
C)  $\ln \left( \frac { x ^ { 3 } ( x - 8 ) } { ( x + 8 ) } \right) ^ { 2 }$ 
D)  $\ln \left( \frac { ( x - 8 ) } { x ^ { 3 } ( x + 8 ) } \right) ^ { 2 }$ 
E)  $\ln \left( \frac { ( x + 8 ) } { x ^ { 3 } ( x - 8 ) } \right) ^ { 2 }$ 
A)  $\ln \left( \frac { x ^ { 3 } } { ( x - 8 ) ( x + 8 ) } \right) ^ { 2 }$ 
B)  $\ln \left( \frac { x ^ { 3 } ( x + 8 ) } { ( x - 8 ) } \right) ^ { 2 }$ 
C)  $\ln \left( \frac { x ^ { 3 } ( x - 8 ) } { ( x + 8 ) } \right) ^ { 2 }$ 
D)  $\ln \left( \frac { ( x - 8 ) } { x ^ { 3 } ( x + 8 ) } \right) ^ { 2 }$ 
E)  $\ln \left( \frac { ( x + 8 ) } { x ^ { 3 } ( x - 8 ) } \right) ^ { 2 }$

Question 16

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 3.6$ .Round to 3 decimal places.

Accepted Answer

A) 5.287 
B) 4.680 
C) 20.055 
D) 2.572 
E) 1.690 
A) 5.287 
B) 4.680 
C) 20.055 
D) 2.572 
E) 1.690

Question 17

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Accepted Answer

A)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$ 
B)  $4 ^ { 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $4 ^ { 1 / 16 } = - 2$ 
E)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$ 
A)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$ 
B)  $4 ^ { 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $4 ^ { 1 / 16 } = - 2$ 
E)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$

Question 18

Simplify the expression.  $6 ^ { \log _ { 6 } 4 }$

Accepted Answer

A) 4 
B) 16 
C) 24 
D) 6 
E) none of these 
A) 4 
B) 16 
C) 24 
D) 6 
E) none of these

Question 19

Write the exponential equation in logarithmic form.   $e ^ { - 0.4 } = 0.670 \ldots$

Accepted Answer

A)  $\ln 0.4 = 0.670$ 
B)  $\ln 0.670 \ldots = 0.4$ 
C)  $\ln 0.670 \ldots = \frac { 1 } { 0.4 }$ 
D)  $\ln 0.670 \ldots = - \frac { 1 } { 0.4 }$ 
E)  $\ln 0.670 \ldots = - 0.4$ 
A)  $\ln 0.4 = 0.670$ 
B)  $\ln 0.670 \ldots = 0.4$ 
C)  $\ln 0.670 \ldots = \frac { 1 } { 0.4 }$ 
D)  $\ln 0.670 \ldots = - \frac { 1 } { 0.4 }$ 
E)  $\ln 0.670 \ldots = - 0.4$

Question 20

$3000 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.)  $r = 0.03$

Accepted Answer

A) 37.62 yr 
B) 36.62 yr 
C) 35.62 yr 
D) 34.62 yr 
E) 38.62 yr 
A) 37.62 yr 
B) 36.62 yr 
C) 35.62 yr 
D) 34.62 yr 
E) 38.62 yr

Use the One-to-One Property to solve the equation for x. $\left( \frac { 1 } { 2 } \right) ^ { x } = 4$

Select the graph of the function. $f ( x ) = 2 ^ { x - 1 }$

Evaluate the function $f ( x ) = \frac { 1 } { 4 } \ln x$ at $x = 4.461$ .Round to 3 decimal places.(You may use your calculator.)

Graph the exponential function. $f ( x ) = 4 ^ { x } + 1$

Assume that x, y, and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } 5 x y$ in terms of the logarithms of x and y.

Solve the equation $\log ( 1 - x ) = \log ( 10 )$ for x using the One-to-One Property.

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 ^ { 8 x } = 2400$

Select the graph of the exponential function. $s ( t ) = 3 e ^ { 0.13 t }$

Match the graph with its exponential function.

Condense the expression to the logarithm of a single quantity. Ln 8 + ln x

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log x = 4$

Select the correct graph for the given function $y = \frac { 6 } { 1 + e ^ { - 2 x } }$

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$

Condense the expression to the logarithm of a single quantity. $2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]$

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 3.6$ .Round to 3 decimal places.

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Simplify the expression. $6 ^ { \log _ { 6 } 4 }$

Write the exponential equation in logarithmic form. $e ^ { - 0.4 } = 0.670 \ldots$

$3000 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.) $r = 0.03$

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

Use the One-to-One Property to solve the equation for x. (12)x=4\left( \frac { 1 } { 2 } \right) ^ { x } = 4(21​)x=4

Select the graph of the function. f(x)=2x−1f ( x ) = 2 ^ { x - 1 }f(x)=2x−1

Evaluate the function f(x)=14ln⁡xf ( x ) = \frac { 1 } { 4 } \ln xf(x)=41​lnx at x=4.461x = 4.461x=4.461 .Round to 3 decimal places.(You may use your calculator.)

Graph the exponential function. f(x)=4x+1f ( x ) = 4 ^ { x } + 1f(x)=4x+1

Assume that x, y, and c are positive numbers.Use the properties of logarithms to write the expression log⁡c5xy\log _ { c } 5 x ylogc​5xy in terms of the logarithms of x and y.

Solve the equation log⁡(1−x)=log⁡(10)\log ( 1 - x ) = \log ( 10 )log(1−x)=log(10) for x using the One-to-One Property.

Solve the exponential equation algebraically.Approximate the result to three decimal places. 38x=24003 ^ { 8 x } = 240038x=2400

Select the graph of the exponential function. s(t)=3e0.13ts ( t ) = 3 e ^ { 0.13 t }s(t)=3e0.13t

Match the graph with its exponential function.

Condense the expression to the logarithm of a single quantity. Ln 8 + ln x

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. log⁡x=4\log x = 4logx=4

Select the correct graph for the given function y=61+e−2xy = \frac { 6 } { 1 + e ^ { - 2 x } }y=1+e−2x6​

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. f(x)=(15)xf ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }f(x)=(51​)x

Condense the expression to the logarithm of a single quantity. 2[3ln⁡x−ln⁡(x+8)−ln⁡(x−8)]2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]2[3lnx−ln(x+8)−ln(x−8)]

Evaluate the function f(x)=1.3xf ( x ) = 1.3 ^ { x }f(x)=1.3x at x=3.6x = 3.6x=3.6 .Round to 3 decimal places.

Rewrite the logarithmic equation log⁡4116=−2\log _ { 4 } \frac { 1 } { 16 } = - 2log4​161​=−2 in exponential form.

Simplify the expression. 6log⁡646 ^ { \log _ { 6 } 4 }6log6​4

Write the exponential equation in logarithmic form. e−0.4=0.670…e ^ { - 0.4 } = 0.670 \ldotse−0.4=0.670…

$3000 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=0.03r = 0.03r=0.03

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

Use the One-to-One Property to solve the equation for x. $\left( \frac { 1 } { 2 } \right) ^ { x } = 4$

Select the graph of the function. $f ( x ) = 2 ^ { x - 1 }$

Evaluate the function $f ( x ) = \frac { 1 } { 4 } \ln x$ at $x = 4.461$ .Round to 3 decimal places.(You may use your calculator.)

Graph the exponential function. $f ( x ) = 4 ^ { x } + 1$

Assume that x, y, and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } 5 x y$ in terms of the logarithms of x and y.

Solve the equation $\log ( 1 - x ) = \log ( 10 )$ for x using the One-to-One Property.

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 ^ { 8 x } = 2400$

Select the graph of the exponential function. $s ( t ) = 3 e ^ { 0.13 t }$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log x = 4$

Select the correct graph for the given function $y = \frac { 6 } { 1 + e ^ { - 2 x } }$

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$

Condense the expression to the logarithm of a single quantity. $2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]$

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 3.6$ .Round to 3 decimal places.

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Simplify the expression. $6 ^ { \log _ { 6 } 4 }$

Write the exponential equation in logarithmic form. $e ^ { - 0.4 } = 0.670 \ldots$

$3000 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.) $r = 0.03$