Question 1

Rewrite the logarithm log4 17 in terms of the natural logarithm.

Accepted Answer

A)  $\frac { \ln 17 } { \log _ { 4 } e }$ 
B)  $\frac { \ln 4 } { \ln 17 }$ 
C)  $\frac { \ln 17 } { \ln 4 }$ 
D) ln 17 
E) ln 4 ln 17 
A)  $\frac { \ln 17 } { \log _ { 4 } e }$ 
B)  $\frac { \ln 4 } { \ln 17 }$ 
C)  $\frac { \ln 17 } { \ln 4 }$ 
D) ln 17 
E) ln 4 ln 17

Question 2

Write the logarithmic equation in exponential form.  $\log _ { 100 } 10 = \frac { 1 } { 2 }$

Accepted Answer

A)  $100 ^ { 1 / 2 } = - 10$ 
B)  $100 ^ { 1 / 2 } = 10$ 
C)  $10 ^ { 1 / 2 } = 100$ 
D)  $100 ^ { 1 / 2 } = - \frac { 1 } { 10 }$ 
E)  $100 ^ { 1 / 2 } = \frac { 1 } { 10 }$ 
A)  $100 ^ { 1 / 2 } = - 10$ 
B)  $100 ^ { 1 / 2 } = 10$ 
C)  $10 ^ { 1 / 2 } = 100$ 
D)  $100 ^ { 1 / 2 } = - \frac { 1 } { 10 }$ 
E)  $100 ^ { 1 / 2 } = \frac { 1 } { 10 }$

Question 3

Solve for x.   $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$

Accepted Answer

A) 4 
B)  $- 3$ 
C) 7 
D) 3 
E)  $- 4$ 
A) 4 
B)  $- 3$ 
C) 7 
D) 3 
E)  $- 4$

Question 4

Evaluate the function at the indicated value of $x = 0.82$ .Round your result to three decimal places. $f ( x ) = 9 \ln x$

Accepted Answer

A) 1.786 
B) -11.674 
C) 0.82 
D) -1.786 
E) 11.674 
A) 1.786 
B) -11.674 
C) 0.82 
D) -1.786 
E) 11.674

Question 5

Rewrite the logarithm as a ratio of common logarithms. 
Log1/7 x

Accepted Answer

A)  $\frac { \log x } { \log \frac { 1 } { 7 } }$ 
B)  $\frac { \log \frac { 1 } { 7 } } { \log x }$ 
C)  $\log \frac { x } { 7 }$ 
D)  $\log 7 x$ 
E) None of these 
A)  $\frac { \log x } { \log \frac { 1 } { 7 } }$ 
B)  $\frac { \log \frac { 1 } { 7 } } { \log x }$ 
C)  $\log \frac { x } { 7 }$ 
D)  $\log 7 x$ 
E) None of these

Question 6

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?

Accepted Answer

A) 17.33 years 
B) 18.33 years 
C) 18.00 years 
D) 17.00 years 
E) 1 year 
A) 17.33 years 
B) 18.33 years 
C) 18.00 years 
D) 17.00 years 
E) 1 year

Question 7

Solve for x.Approximate the result to three decimal places.  $e ^ { x } = 4$

Accepted Answer

A)  $\ln 4 \approx 1.466$ 
B)  $\ln 4 \approx 1.476$ 
C)  $\ln 4 \approx 1.436$ 
D)  $\ln 4 \approx 1.386$ 
E)  $\ln 4 \approx 1.456$ 
A)  $\ln 4 \approx 1.466$ 
B)  $\ln 4 \approx 1.476$ 
C)  $\ln 4 \approx 1.436$ 
D)  $\ln 4 \approx 1.386$ 
E)  $\ln 4 \approx 1.456$

Question 8

Write the exponential equation in logarithmic form.   $e ^ { 3 x } = 4$

Accepted Answer

A)  $\ln 4 = - 3 x$ 
B)  $\ln 4 = - \frac { 1 } { 3 } x$ 
C)  $\ln 4 = \frac { 1 } { 3 } x$ 
D)  $\ln 4 = 3 x$ 
E)  $\ln 3 = 4 x$ 
A)  $\ln 4 = - 3 x$ 
B)  $\ln 4 = - \frac { 1 } { 3 } x$ 
C)  $\ln 4 = \frac { 1 } { 3 } x$ 
D)  $\ln 4 = 3 x$ 
E)  $\ln 3 = 4 x$

Question 9

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.  $8 + 71 \ln x = 14$

Accepted Answer

A)  $e ^ { 6 / 7 } \approx 3.356$ 
B)  $e ^ { 6 / 7 } \approx 1.356$ 
C)  $e ^ { 6 / 7 } \approx 4.356$ 
D)  $e ^ { 6 / 7 } \approx 2.356$ 
E)  $e ^ { 6 / 7 } \approx 0.356$ 
A)  $e ^ { 6 / 7 } \approx 3.356$ 
B)  $e ^ { 6 / 7 } \approx 1.356$ 
C)  $e ^ { 6 / 7 } \approx 4.356$ 
D)  $e ^ { 6 / 7 } \approx 2.356$ 
E)  $e ^ { 6 / 7 } \approx 0.356$

Question 10

What is the value of the function $f ( x ) = 4.8 e ^ { - 1.7 x }$ at $x = 2.5$ ? Round to 3 decimal places.

Accepted Answer

A) 10.683 
B) 0.000 
C) -55.453 
D) 0.877 
E) 0.068 
A) 10.683 
B) 0.000 
C) -55.453 
D) 0.877 
E) 0.068

Question 11

Use a graphing utility to determine which graph below is the graph of the function.  
  $g ( x ) = 0.1 e ^ { - 4 x }$

Accepted Answer

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

Question 12

Find the exact value of $\ln e ^ { 250 } - \ln \sqrt { e }$ without using a calculator.

Accepted Answer

A) 5 
B) 2.5 
C) 1.25 
D) 2 
E) 3 
A) 5 
B) 2.5 
C) 1.25 
D) 2 
E) 3

Question 13

Evaluate the function at the indicated value of x.Round your result to three decimal places. 
Function
Value $h ( x ) = e ^ { - x }$ $x = \frac { 5 } { 8 }$

Accepted Answer

A)  $8.07$ 
B)  $0.625$ 
C)  $1.148$ 
D)  $5.500$ 
E)  $0.535$ 
A)  $8.07$ 
B)  $0.625$ 
C)  $1.148$ 
D)  $5.500$ 
E)  $0.535$

Question 14

Graph the function. $f ( x ) = 3 ^ { x }$

Accepted Answer

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

Question 15

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) = log11.7 x

Accepted Answer

A)  $f ( x ) = \frac { \log x } { \log 11.7 } = \frac { \ln x } { \ln 11.7 }$   
B)  $f ( x ) = \frac { \log 11.7 } { \log x } = \frac { \ln 11.7 } { \ln x }$   
C) f(x) = log x  + log 11.7 = ln x  + ln 11.7   
D)  $f ( x ) = \log \frac { 11.7 } { x } = \ln \frac { 11.7 } { x }$   
E)  $f ( x ) = \log \frac { x } { 11.7 } = \ln \frac { x } { 11.7 }$    
A)  $f ( x ) = \frac { \log x } { \log 11.7 } = \frac { \ln x } { \ln 11.7 }$   
B)  $f ( x ) = \frac { \log 11.7 } { \log x } = \frac { \ln 11.7 } { \ln x }$   
C) f(x) = log x  + log 11.7 = ln x  + ln 11.7   
D)  $f ( x ) = \log \frac { 11.7 } { x } = \ln \frac { 11.7 } { x }$   
E)  $f ( x ) = \log \frac { x } { 11.7 } = \ln \frac { x } { 11.7 }$

Question 16

Use the properties of logarithms to simplify the expression.  $\log _ { 5 } 5 ^ { 5 }$

Accepted Answer

A) 0 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D) -5 
E) 5 
A) 0 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D) -5 
E) 5

Question 17

Solve for x.Approximate the result to three decimal places.  $\ln x = - 2$

Accepted Answer

A)  $e ^ { - 2 } \approx 7.389$ 
B)  $e ^ { - 2 } \approx 0.368$ 
C)  $e ^ { - 2 } \approx 2.718$ 
D)  $e ^ { - 2 } \approx 0.135$ 
E)  $e ^ { - 2 } \approx 1.000$ 
A)  $e ^ { - 2 } \approx 7.389$ 
B)  $e ^ { - 2 } \approx 0.368$ 
C)  $e ^ { - 2 } \approx 2.718$ 
D)  $e ^ { - 2 } \approx 0.135$ 
E)  $e ^ { - 2 } \approx 1.000$

Question 18

Use a graphing utility to determine which graph below is the graph of the function. $s ( x ) = 1.1 e ^ { - ( x - 1 ) ^ { 2 } }$

Accepted Answer

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

Question 19

Write the exponential equation in logarithmic form.  $81 ^ { 1 / 2 } = 9$

Accepted Answer

A)  $\log _ { 81 } 9 = \frac { 1 } { 2 }$ 
B)  $\log _ { 81 } \frac { 1 } { 2 } = 9$ 
C)  $\log _ { 81 } 9 = 2$ 
D)  $\log _ { 81 } 9 = - \frac { 1 } { 2 }$ 
E)  $\log _ { 9 } 81 = \frac { 1 } { 2 }$ 
A)  $\log _ { 81 } 9 = \frac { 1 } { 2 }$ 
B)  $\log _ { 81 } \frac { 1 } { 2 } = 9$ 
C)  $\log _ { 81 } 9 = 2$ 
D)  $\log _ { 81 } 9 = - \frac { 1 } { 2 }$ 
E)  $\log _ { 9 } 81 = \frac { 1 } { 2 }$

Question 20

An initial investment of $5000 doubles in value in 6.3 years.Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

Accepted Answer

A) 11.0% 
B) 4.8% 
C) 5.5% 
D) 6.3% 
E) 100% 
A) 11.0% 
B) 4.8% 
C) 5.5% 
D) 6.3% 
E) 100%

Rewrite the logarithm log₄ 17 in terms of the natural logarithm.

Write the logarithmic equation in exponential form. $\log _ { 100 } 10 = \frac { 1 } { 2 }$

Solve for x. $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$

Evaluate the function at the indicated value of $x = 0.82$ .Round your result to three decimal places. $f ( x ) = 9 \ln x$

Rewrite the logarithm as a ratio of common logarithms. Log_1/7 x

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?

Solve for x.Approximate the result to three decimal places. $e ^ { x } = 4$

Write the exponential equation in logarithmic form. $e ^ { 3 x } = 4$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $8 + 71 \ln x = 14$

What is the value of the function $f ( x ) = 4.8 e ^ { - 1.7 x }$ at $x = 2.5$ ? Round to 3 decimal places.

Use a graphing utility to determine which graph below is the graph of the function. $g ( x ) = 0.1 e ^ { - 4 x }$

Find the exact value of $\ln e ^ { 250 } - \ln \sqrt { e }$ without using a calculator.

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $h ( x ) = e ^ { - x }$ $x = \frac { 5 } { 8 }$

Graph the function. $f ( x ) = 3 ^ { x }$

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) = log_11.7 x

Use the properties of logarithms to simplify the expression. $\log _ { 5 } 5 ^ { 5 }$

Solve for x.Approximate the result to three decimal places. $\ln x = - 2$

Use a graphing utility to determine which graph below is the graph of the function. $s ( x ) = 1.1 e ^ { - ( x - 1 ) ^ { 2 } }$

Write the exponential equation in logarithmic form. $81 ^ { 1 / 2 } = 9$

An initial investment of $5000 doubles in value in 6.3 years.Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

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

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Exam 3: Exponential and Logarithmic Functions

Rewrite the logarithm log4 17 in terms of the natural logarithm.

Write the logarithmic equation in exponential form. log⁡10010=12\log _ { 100 } 10 = \frac { 1 } { 2 }log100​10=21​

Solve for x. (14)x=64\left( \frac { 1 } { 4 } \right) ^ { x } = 64(41​)x=64

Evaluate the function at the indicated value of x=0.82x = 0.82x=0.82 .Round your result to three decimal places. f(x)=9ln⁡xf ( x ) = 9 \ln xf(x)=9lnx

Rewrite the logarithm as a ratio of common logarithms. Log1/7 x

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?

Solve for x.Approximate the result to three decimal places. ex=4e ^ { x } = 4ex=4

Write the exponential equation in logarithmic form. e3x=4e ^ { 3 x } = 4e3x=4

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. 8+71ln⁡x=148 + 71 \ln x = 148+71lnx=14

What is the value of the function f(x)=4.8e−1.7xf ( x ) = 4.8 e ^ { - 1.7 x }f(x)=4.8e−1.7x at x=2.5x = 2.5x=2.5 ? Round to 3 decimal places.

Use a graphing utility to determine which graph below is the graph of the function. g(x)=0.1e−4xg ( x ) = 0.1 e ^ { - 4 x }g(x)=0.1e−4x

Find the exact value of ln⁡e250−ln⁡e\ln e ^ { 250 } - \ln \sqrt { e }lne250−lne​ without using a calculator.

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value h(x)=e−xh ( x ) = e ^ { - x }h(x)=e−x x=58x = \frac { 5 } { 8 }x=85​

Graph the function. f(x)=3xf ( x ) = 3 ^ { x }f(x)=3x

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) = log11.7 x

Use the properties of logarithms to simplify the expression. log⁡555\log _ { 5 } 5 ^ { 5 }log5​55

Solve for x.Approximate the result to three decimal places. ln⁡x=−2\ln x = - 2lnx=−2

Use a graphing utility to determine which graph below is the graph of the function. s(x)=1.1e−(x−1)2s ( x ) = 1.1 e ^ { - ( x - 1 ) ^ { 2 } }s(x)=1.1e−(x−1)2

Write the exponential equation in logarithmic form. 811/2=981 ^ { 1 / 2 } = 9811/2=9

An initial investment of $5000 doubles in value in 6.3 years.Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

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

Rewrite the logarithm log₄ 17 in terms of the natural logarithm.

Write the logarithmic equation in exponential form. $\log _ { 100 } 10 = \frac { 1 } { 2 }$

Solve for x. $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$

Evaluate the function at the indicated value of $x = 0.82$ .Round your result to three decimal places. $f ( x ) = 9 \ln x$

Rewrite the logarithm as a ratio of common logarithms. Log_1/7 x

Solve for x.Approximate the result to three decimal places. $e ^ { x } = 4$

Write the exponential equation in logarithmic form. $e ^ { 3 x } = 4$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $8 + 71 \ln x = 14$

What is the value of the function $f ( x ) = 4.8 e ^ { - 1.7 x }$ at $x = 2.5$ ? Round to 3 decimal places.

Use a graphing utility to determine which graph below is the graph of the function. $g ( x ) = 0.1 e ^ { - 4 x }$

Find the exact value of $\ln e ^ { 250 } - \ln \sqrt { e }$ without using a calculator.

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $h ( x ) = e ^ { - x }$ $x = \frac { 5 } { 8 }$

Graph the function. $f ( x ) = 3 ^ { x }$

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) = log_11.7 x

Use the properties of logarithms to simplify the expression. $\log _ { 5 } 5 ^ { 5 }$

Solve for x.Approximate the result to three decimal places. $\ln x = - 2$

Use a graphing utility to determine which graph below is the graph of the function. $s ( x ) = 1.1 e ^ { - ( x - 1 ) ^ { 2 } }$

Write the exponential equation in logarithmic form. $81 ^ { 1 / 2 } = 9$