# 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 (2,480 points)

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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 (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.

answered 3 years ago (11,780 points)

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