What is the smallest integer n for which 25^n > 5^12 ?  Choose the correct choice from the following answers.
A) 6 B) 7 C) 8 D) 9 E) 10
To solve, we want to get the bases the same. Thus we need to break 25^n into prime factors.   25^n = (5^2)^n = 5^(2n) (Remember that when we have a power to a power, we multiply the exponents.)   We can use the new value in the given inequality:   5^(2n)&gt; 5^12   Since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents.   2n &gt; 12   n &gt; 6   Because n is greater than 6, the smallest integer that satisfies the inequality 25^n &gt; 5^12 is 7.   The answer is 7.
<result>B</result>
What is the smallest integer n for which 25^n > 5^12 ?