Question 1

Condense the expression to the logarithm of a single quantity. 
Log x - 2log y + 3log z

Accepted Answer

A)  $\log \frac { z ^ { 3 } } { x y ^ { 2 } }$ 
B)  $\log \frac { x } { y ^ { 2 } z ^ { 3 } }$ 
C)  $\log \frac { x y ^ { 2 } } { z ^ { 3 } }$ 
D)  $\log \frac { y ^ { 2 } } { x z ^ { 3 } }$ 
E)  $\log \frac { x z ^ { 3 } } { y ^ { 2 } }$ 
A)  $\log \frac { z ^ { 3 } } { x y ^ { 2 } }$ 
B)  $\log \frac { x } { y ^ { 2 } z ^ { 3 } }$ 
C)  $\log \frac { x y ^ { 2 } } { z ^ { 3 } }$ 
D)  $\log \frac { y ^ { 2 } } { x z ^ { 3 } }$ 
E)  $\log \frac { x z ^ { 3 } } { y ^ { 2 } }$

Question 2

An initial investment of $4000 grows at an annual interest rate of 5% compounded continuously.How long will it take to double the investment?

Accepted Answer

A) 1 year 
B) 14.40 years 
C) 13.86 years 
D) 14.86 years 
E) 13.40 years 
A) 1 year 
B) 14.40 years 
C) 13.86 years 
D) 14.86 years 
E) 13.40 years

Question 3

Simplify the expression log5 175.

Accepted Answer

A) 35log5 2 
B) 2 log5 7 
C) 7 
D) ​2 + log5 7 
E) The expression cannot be simplified. 
A) 35log5 2 
B) 2 log5 7 
C) 7 
D) ​2 + log5 7 
E) The expression cannot be simplified.

Question 4

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 30% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.

Accepted Answer

A) 28,040 years 
B) 5715 years 
C) 9926 years 
D) 14,758 years 
E) 100 years 
A) 28,040 years 
B) 5715 years 
C) 9926 years 
D) 14,758 years 
E) 100 years

Question 5

Write the logarithmic equation in exponential form.   $\ln ( 8 ) = 2.079 \ldots$

Accepted Answer

A)  $e ^ { - 2079 \cdots } = - 8$ 
B)  $e ^ { - 2079 \cdots } = 8$ 
C)  $e ^ { 2.079 \cdots } = - 8$ 
D)  $e ^ { 2.079 \ldots } = \frac { 1 } { 8 }$ 
E)  $e ^ { 2.079 \cdots } = 8$ 
A)  $e ^ { - 2079 \cdots } = - 8$ 
B)  $e ^ { - 2079 \cdots } = 8$ 
C)  $e ^ { 2.079 \cdots } = - 8$ 
D)  $e ^ { 2.079 \ldots } = \frac { 1 } { 8 }$ 
E)  $e ^ { 2.079 \cdots } = 8$

Question 6

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.  $x = 70.75$

Accepted Answer

A) 1.85 
B) 0.541 
C) 0.014 
D) -0.541 
E) -1.85 
A) 1.85 
B) 0.541 
C) 0.014 
D) -0.541 
E) -1.85

Question 7

After t years, the value of a wheelchair conversion van that originally cost $39,000 depreciates so that each year it is worth $\frac { 7 } { 8 }$ of its value for the previous year.Find a model for V(t), the value of the van after t years.

Accepted Answer

A)  $V ( t ) = - 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$ 
B)  $V ( t ) = 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$ 
C)  $V ( t ) = - 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$ 
D)  $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$ 
E)  $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { - t }$ 
A)  $V ( t ) = - 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$ 
B)  $V ( t ) = 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$ 
C)  $V ( t ) = - 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$ 
D)  $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$ 
E)  $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { - t }$

Question 8

Find the magnitude R of an earthquake of intensity $\left. I \text { (let } I _ { 0 } = 1 \right)$ .  $I = 270300000$

Accepted Answer

A) 7.43 
B) 6.43 
C) 8.43 
D) 10.43 
E) 9.43 
A) 7.43 
B) 6.43 
C) 8.43 
D) 10.43 
E) 9.43

Question 9

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Accepted Answer

A)  $\frac { 3 } { 49 }$ 
B)  $\frac { 14 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D) -1 
E)  $\frac { 49 } { 3 }$ 
A)  $\frac { 3 } { 49 }$ 
B)  $\frac { 14 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D) -1 
E)  $\frac { 49 } { 3 }$

Question 10

The population P (in thousands) of Reno, Nevada from 2000 through 2007 can be modeled by $P = 346.8 e ^ { k t }$ where t represents the year, with $t = 0$ corresponding to 2000.In 2005, the population of Reno was about 395,000.According to the model, during what year will the population reach 486,000.00?

Accepted Answer

A) 2013 
B) 2005 
C) 2021 
D) 2017 
E) 2009 
A) 2013 
B) 2005 
C) 2021 
D) 2017 
E) 2009

Question 11

Select the graph of the function.  $f ( x ) = 4 e ^ { x + 5 }$

Accepted Answer

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

Question 12

Evaluate the logarithm log1/3 0.603 using the change of base formula.Round to 3 decimal places.

Accepted Answer

A) 2.172 
B) 0.556 
C) -0.506 
D) -0.22 
E) 0.46 
A) 2.172 
B) 0.556 
C) -0.506 
D) -0.22 
E) 0.46

Question 13

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$ .

Accepted Answer

A) 3 
B) 0 
C) -9 
D) -81 
E) The expression cannot be simplified. 
A) 3 
B) 0 
C) -9 
D) -81 
E) The expression cannot be simplified.

Question 14

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Accepted Answer

A) 0 
B) -1 
C) -2 
D) 2 
E)  $\frac { 1 } { 2 }$ 
A) 0 
B) -1 
C) -2 
D) 2 
E)  $\frac { 1 } { 2 }$

Question 15

The line $y = - 5$ is an asymptote for the graph of $f ( x ) = 10 ^ { x } - 5$

Accepted Answer

A) True 
 B)False

Question 16

Evaluate the function at the indicated value of x.Round your result to three decimal places. 
Function
Value $h ( x ) = 400 e ^ { 0.05 x }$ $x = 15$

Accepted Answer

A)  $846.800$ 
B)  $1046.800$ 
C)  $1246.800$ 
D)  $946.800$ 
E)  $1146.800$ 
A)  $846.800$ 
B)  $1046.800$ 
C)  $1246.800$ 
D)  $946.800$ 
E)  $1146.800$

Question 17

Select the graph of the exponential function.  $g ( x ) = 6 + e ^ { - x }$

Accepted Answer

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

Question 18

Find the exact value of the logarithmic expression without using a calculator. ​
Log6 216
​

Accepted Answer

A) 3 
B) 6 
C) 216 
D) 35 
E) None of these 
A) 3 
B) 6 
C) 216 
D) 35 
E) None of these

Question 19

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) 
Ln 9x

Accepted Answer

A) ln 9 - ln x 
B)  $\frac { \ln 9 } { \ln x }$ 
C) ln 9 × ln x 
D) ln 9 + ln x 
E) None of these 
A) ln 9 - ln x 
B)  $\frac { \ln 9 } { \ln x }$ 
C) ln 9 × ln x 
D) ln 9 + ln x 
E) None of these

Question 20

Evaluate the function $f ( x ) = \log _ { 5 } x$ at $x = \frac { 1 } { 25 }$ without using a calculator.

Accepted Answer

A)  $\frac { 1 } { 25 }$ 
B) -3 
C) -1 
D) 25 
E) -2 
A)  $\frac { 1 } { 25 }$ 
B) -3 
C) -1 
D) 25 
E) -2

Condense the expression to the logarithm of a single quantity. Log x - 2log y + 3log z

An initial investment of $4000 grows at an annual interest rate of 5% compounded continuously.How long will it take to double the investment?

Simplify the expression log₅ 175.

Write the logarithmic equation in exponential form. $\ln ( 8 ) = 2.079 \ldots$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = 70.75$

After t years, the value of a wheelchair conversion van that originally cost $39,000 depreciates so that each year it is worth $\frac { 7 } { 8 }$ of its value for the previous year.Find a model for V(t), the value of the van after t years.

Find the magnitude R of an earthquake of intensity $\left. I \text { (let } I _ { 0 } = 1 \right)$ . $I = 270300000$

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Select the graph of the function. $f ( x ) = 4 e ^ { x + 5 }$

Evaluate the logarithm log_1/3 0.603 using the change of base formula.Round to 3 decimal places.

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$ .

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

The line $y = - 5$ is an asymptote for the graph of $f ( x ) = 10 ^ { x } - 5$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $h ( x ) = 400 e ^ { 0.05 x }$ $x = 15$

Select the graph of the exponential function. $g ( x ) = 6 + e ^ { - x }$

Find the exact value of the logarithmic expression without using a calculator. Log₆ 216

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) Ln 9x

Evaluate the function $f ( x ) = \log _ { 5 } x$ at $x = \frac { 1 } { 25 }$ without using a calculator.

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

Condense the expression to the logarithm of a single quantity. Log x - 2log y + 3log z

An initial investment of $4000 grows at an annual interest rate of 5% compounded continuously.How long will it take to double the investment?

Simplify the expression log5 175.

Write the logarithmic equation in exponential form. ln⁡(8)=2.079…\ln ( 8 ) = 2.079 \ldotsln(8)=2.079…

Evaluate f(x)=log⁡xf ( x ) = \log xf(x)=logx at the indicated value of x.Round your result to three decimal places. x=70.75x = 70.75x=70.75

After t years, the value of a wheelchair conversion van that originally cost $39,000 depreciates so that each year it is worth 78\frac { 7 } { 8 }87​ of its value for the previous year.Find a model for V(t), the value of the van after t years.

Find the magnitude R of an earthquake of intensity I (let I0=1)\left. I \text { (let } I _ { 0 } = 1 \right)I (let I0​=1) . I=270300000I = 270300000I=270300000

Find the exact value of log⁡7493\log _ { 7 } \sqrt [ 3 ] { 49 }log7​349​ without using a calculator.

Select the graph of the function. f(x)=4ex+5f ( x ) = 4 e ^ { x + 5 }f(x)=4ex+5

Evaluate the logarithm log1/3 0.603 using the change of base formula.Round to 3 decimal places.

Simplify the expression log⁡3(127)3\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }log3​(271​)3 .

Evaluate the function f(x)=log⁡2xf ( x ) = \log _ { 2 } xf(x)=log2​x at x=12x = \frac { 1 } { 2 }x=21​ without using a calculator.

The line y=−5y = - 5y=−5 is an asymptote for the graph of f(x)=10x−5f ( x ) = 10 ^ { x } - 5f(x)=10x−5

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value h(x)=400e0.05xh ( x ) = 400 e ^ { 0.05 x }h(x)=400e0.05x x=15x = 15x=15

Select the graph of the exponential function. g(x)=6+e−xg ( x ) = 6 + e ^ { - x }g(x)=6+e−x

Find the exact value of the logarithmic expression without using a calculator. ​ Log6 216 ​

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) Ln 9x

Evaluate the function f(x)=log⁡5xf ( x ) = \log _ { 5 } xf(x)=log5​x at x=125x = \frac { 1 } { 25 }x=251​ without using a calculator.

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

Simplify the expression log₅ 175.

Write the logarithmic equation in exponential form. $\ln ( 8 ) = 2.079 \ldots$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = 70.75$

After t years, the value of a wheelchair conversion van that originally cost $39,000 depreciates so that each year it is worth $\frac { 7 } { 8 }$ of its value for the previous year.Find a model for V(t), the value of the van after t years.

Find the magnitude R of an earthquake of intensity $\left. I \text { (let } I _ { 0 } = 1 \right)$ . $I = 270300000$

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Select the graph of the function. $f ( x ) = 4 e ^ { x + 5 }$

Evaluate the logarithm log_1/3 0.603 using the change of base formula.Round to 3 decimal places.

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$ .

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

The line $y = - 5$ is an asymptote for the graph of $f ( x ) = 10 ^ { x } - 5$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $h ( x ) = 400 e ^ { 0.05 x }$ $x = 15$

Select the graph of the exponential function. $g ( x ) = 6 + e ^ { - x }$

Find the exact value of the logarithmic expression without using a calculator. Log₆ 216

Evaluate the function $f ( x ) = \log _ { 5 } x$ at $x = \frac { 1 } { 25 }$ without using a calculator.