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powers

This topic has 1 expert reply and 2 member replies

powers

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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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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

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isn't there a way to solve this problem fast,,,

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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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