GHong14 wrote:If n is an integer, what is the least possible value of n such that 40,000,000 < 5n ?
a 7
b 8
c 9
d 10
e 11
Correct Answer is e
Another approach is try to get similar bases on each side of the inequality:
5^n > 40,000,000
5^n > 4 * 10^7
5^n > 2^2 * 2^7* 5^7
5^n > 2^9 * 5^7
5^n > 512 * 5^7
Rewriting the left side to look like the right side, we get:
5^x * 5^7 > 512 * 5^7.
Since on the right side we have 512, on the left side we need 5^x = 5^4 = 625 in order to make the left side larger:
5^4 * 5^7 > 512 * 5^7
5^11 > 512 * 5^7
Thus, n = 11.
The correct answer is
E.
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