TASK DEFINITION: In this task, you need to provide the correct option for a given problem from the provided options.
PROBLEM: Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30

SOLUTION: d

PROBLEM: Problem: the duplicate ratio of 6 : 4 is ? 
Options: a ) 1 : 2 , b ) 9 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13

SOLUTION: b

PROBLEM: Problem: the value of ( log 9 27 + log 8 32 ) is : 
Options: a ) 7 / 2 , b ) 19 / 6 , c ) 5 / 3 , d ) 7 , e ) 8

SOLUTION:
c