powers

[sumasajja]

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

[vineeshp]

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

[sumasajja]

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

[Anurag@Gurome]

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.