A+ Answers

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, ∞)