Question 1

Rewrite the logarithm log6 412 in terms of the common logarithm (base 10).

Accepted Answer

A) log 6 log 412 
B)    
C)    
D) log 412 
E)    
A) log 6 log 412 
B)    
C)    
D) log 412 
E)

Question 2

Evaluate the function   at   .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 3

Solve for x. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) 5 
A)    
B)    
C)    
D)    
E) 5

Question 4

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

Accepted Answer

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

Question 5

Select the graph of the exponential function. ​   ​

Accepted Answer

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

Question 6

Evaluate the function at the indicated value of   .Round your result to three decimal places. ​   ​

Accepted Answer

A) -1.386 
B) 4 
C) 2.079 
D) -2.079 
E) 1.386 
A) -1.386 
B) 4 
C) 2.079 
D) -2.079 
E) 1.386

Question 7

Write the logarithmic equation in exponential form. ​   ​

Accepted Answer

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

Question 8

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
​
Log15 1,500
​

Accepted Answer

A) 5.701 
B) 3.701 
C) 2.701 
D) 6.701 
E) 4.701 
A) 5.701 
B) 3.701 
C) 2.701 
D) 6.701 
E) 4.701

Question 9

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​   ​

Accepted Answer

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

Question 10

What is the value of the function   at   ? Round to 3 decimal places.

Accepted Answer

A) 376.394 
B) 223.774 
C) 18.232 
D) 151.492 
E) 1247.646 
A) 376.394 
B) 223.774 
C) 18.232 
D) 151.492 
E) 1247.646

Question 11

Use properties of exponents to determine which functions (if any) are the same. ​   ​

Accepted Answer

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

Question 12

The population P (in thousands) of Reno, Nevada from 2000 through 2007 can be modeled by   where t represents the year, with   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 13

Evaluate the function   at   .Round to 3 decimal places.(You may use your calculator.)

Accepted Answer

A) -5.201 
B) 5.201 
C) undefined 
D) -2.709 
E) 0.369 
A) -5.201 
B) 5.201 
C) undefined 
D) -2.709 
E) 0.369

Question 14

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   , 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 15

$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.) ​   ​

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 16

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

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 17

The chemical acidity of a solution is measured in units of pH:   , where   is the hydrogen ion concentration in the solution.What is   if the   ?

Accepted Answer

A)    
B)    
C)    
D)    
E) 6.800 
A)    
B)    
C)    
D)    
E) 6.800

Question 18

Find the exact value of   without using a calculator.

Accepted Answer

A)    
B)    
C)    
D) -1 
E)    
A)    
B)    
C)    
D) -1 
E)

Question 19

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   , 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 20

Write the logarithmic equation in exponential form. ​   ​

Accepted Answer

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

Rewrite the logarithm log₆ 412 in terms of the common logarithm (base 10).

Evaluate the function at .Round to 3 decimal places.

Solve for x.

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

Select the graph of the exponential function.

Evaluate the function at the indicated value of .Round your result to three decimal places.

Write the logarithmic equation in exponential form.

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₁₅ 1,500

Solve the exponential equation algebraically.Approximate the result to three decimal places.

What is the value of the function at ? Round to 3 decimal places.

Use properties of exponents to determine which functions (if any) are the same.

The population P (in thousands) of Reno, Nevada from 2000 through 2007 can be modeled by where t represents the year, with 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?

Evaluate the function at .Round to 3 decimal places.(You may use your calculator.)

$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.)

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

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.What is if the ?

Find the exact value of without using a calculator.

Write the logarithmic equation in exponential form.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 5: Exponential-And-Logarithmic-Functions

Rewrite the logarithm log6 412 in terms of the common logarithm (base 10).

Evaluate the function at .Round to 3 decimal places.

Solve for x. ​ ​

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

Select the graph of the exponential function. ​ ​

Evaluate the function at the indicated value of .Round your result to three decimal places. ​ ​

Write the logarithmic equation in exponential form. ​ ​

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log15 1,500 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

What is the value of the function at ? Round to 3 decimal places.

Use properties of exponents to determine which functions (if any) are the same. ​ ​

The population P (in thousands) of Reno, Nevada from 2000 through 2007 can be modeled by where t represents the year, with 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? ​

Evaluate the function at .Round to 3 decimal places.(You may use your calculator.)

$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.) ​ ​

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

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.What is if the ?

Find the exact value of without using a calculator.

Write the logarithmic equation in exponential form. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Topics-In-Analytic-Geometry

Prerequisites

Filters

Rewrite the logarithm log₆ 412 in terms of the common logarithm (base 10).

Solve for x.

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

Select the graph of the exponential function.

Evaluate the function at the indicated value of .Round your result to three decimal places.

Write the logarithmic equation in exponential form.

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₁₅ 1,500

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Use properties of exponents to determine which functions (if any) are the same.

The population P (in thousands) of Reno, Nevada from 2000 through 2007 can be modeled by where t represents the year, with 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?

$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.)

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

Write the logarithmic equation in exponential form.