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by sumasajja » Wed Jul 27, 2011 7:03 pm
if k is an integer and 5 to the power of k < 20,000. what is the greatest possible value of k?
a] 6
b] 7
c] 8
d] 9
e] 10
the answer is
a i.e. 6
Last edited by sumasajja on Wed Jul 27, 2011 7:59 pm, edited 1 time in total.
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by vineeshp » Wed Jul 27, 2011 7:48 pm
k ^ 5 < 20000

6 ^ 5 = ^ * 1296... somewhere near 7800.

7 ^ 5 = 343 * 49 = 16000

which means 8 6 5 will go over 20000.

I guess the question meant 5 TO the power of k. 5 ^ 6 = 15625.

5 ^ 7 will take it over 20,000
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by sumasajja » Wed Jul 27, 2011 8:08 pm
isn't there a way to solve this problem fast,,,
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by Anurag@Gurome » Wed Jul 27, 2011 8:49 pm
sumasajja wrote:if k is an integer and 5 power of k < 20,000. what is the greatest possible value of k?
a] 6
b] 7
c] 8
d] 9
e] 10
the answer is
a i.e. 6
5^k < 20,000
20,000 = (2^5)*(5^4)
Now, 5² < 2^5 or (5²)*(5^4) < (2^5)*(5^4) or (5^6) < 20,000
So, 5^k < 20,000 implies k = 6

The correct answer is A.
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