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The smallest integer...

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What is the smallest integer n for which \(25^{n}>5^{12}\) ?

A. 6
B. 7
C. 8
D. 9
E. 10
asked 3 years ago in Ration & Proportion by surya (2,480 points)

2 Answers

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the option is B (7) because:
the given condition is \(25^{n}\) > \(5^{12}\)
                               
                                \(5^{2n}\) > \(5^{12}\)

                                              2n > 12

                                               n > 6
      
   the least integer after 6 is 7
answered 3 years ago by sravanthi (4,200 points)
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Because \(5^{2}\) = 25, a common base is 5 .Rewrite the left side with 5 as a base : \(25^{n}\) = \((5^{2})^{n}\)=\(5^{2n}\).
It follows that the desired integer is the least integher n for which \(5^{2n}\) > \(5^{12}\). This will be the least integer n for which 2n > 12, or the least integer n for which n > 6 , which is 7.
 
Hence, the answer is B(7).
answered 3 years ago by fasttrack (11,780 points)

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