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Question 1          

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.

3^1-x = 1/27
A. {2}     

B. {-7}   

C. {4}    

D. {3}     
Question 2          

Write the following equation in its equivalent exponential form.



5 = log_b 32
A. b⁵ = 32            

B. y⁵ = 32            

C. B^log5 = 32        

D. Log^b = 32        
Question 3          

Use properties of logarithms to expand the following logarithmic expression as much as possible.



Log_b (√xy³ / z³)
A. 1/2 log_b x - 6 log_b y + 3 log_b z     

B. 1/2 log_b x - 9 log_b y - 3 log_b z     

C. 1/2 log_b x + 3 log_b y + 6 log_b z   

D. 1/2 log_b x + 3 log_b y - 3 log_b z     
Question 4          

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution.

3^2x + 3^x - 2 = 0
A. {1}     

B. {-2}   

C. {5}    

D. {0}     
Question 5          

Write the following equation in its equivalent logarithmic form.

3√8 = 2
A. Log₂ 3 = 1/8   

B. Log₈ 2 = 1/3   

C. Log₂ 8 = 1/2   

D. Log₃ 2 = 1/8    
Question 6          

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution.

e^x = 5.7
A. {ln 5.7}; ≈1.74

B. {ln 8.7}; ≈3.74

C. {ln 6.9}; ≈2.49

D. {ln 8.9}; ≈3.97 
Question 7          

Write the following equation in its equivalent exponential form.



log₆ 216 = y
A. 6^y = 216          

B. 6^x = 216          

C. 6^logy = 224      

D. 6^xy = 232         
Question 8          

Use properties of logarithms to expand the following logarithmic expression as much as possible.

log_b (x²y)
A. 2 log_y x + log_x y             

B. 2 log_b x + log_b y            

C. log_x - log_b y    

D. log_b x – log_x y  
Question 9          

An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams              

B. Approximately 8 grams              

C. Approximately 23 grams           

D. Approximately 4 grams              
Question 10        

Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.

2 log x = log 25
A. {12}  

B. {5}     

C. {-3}   

D. {25}   
Question 11        

Evaluate the following expression without using a calculator.

Log₇ √7
A. 1/4    

B. 3/5    

C. 1/2    

D. 2/7     
Question 12        

Write the following equation in its equivalent logarithmic form.

2^-4 = 1/16
A. Log₄ 1/16 = 64              

B. Log₂ 1/24 = -4

C. Log₂ 1/16 = -4              

D. Log₄ 1/16 = 54              
Question 13        

Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.

log₂ 96 – log² 3
A. 5       

B. 7       

C. 12     

D. 4        
Question 14        

The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds?
A. 10 grams after 10 seconds; 6 grams after 20 seconds     

B. 12 grams after 10 seconds; 7 grams after 20 seconds     

C. 4 grams after 10 seconds; 1 gram after 20 seconds         

D. 8 grams after 10 seconds; 4 grams after 20 seconds        
Question 15        

Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.

log x + 3 log y
A. log (xy)           

B. log (xy³)          

C. log (xy²)          

D. log_y (xy)³         
Question 16        

Write the following equation in its equivalent exponential form.



4 = log² 16
A. 2 log₄ = 16     

B. 2² = 4              

C. 4⁴ = 256         

D. 2⁴ = 16             
Question 17        

Approximate the following using a calculator; round your answer to three decimal places.

3^√5
A. .765  

B. 14297             

C. 11.494            

D. 11.665             
Question 18        

Approximate the following using a calculator; round your answer to three decimal places.

e^-0.95
A. .483  

B. 1.287              

C. .597 

D. .387  
Question 19        

The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)          

B. bx; (-∞, -∞); (2, ∞)         

C. bx; (-∞, ∞); (0, ∞)          

D. bx; (-∞, -∞); (-1, ∞)         
Question 20        

Find the domain of following logarithmic function.

f(x) = log₅ (x + 4)
A. (-4, ∞)              

B. (-5, -∞)            

C. (7, -∞)             

D. (-9, ∞)