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# If x and y are none negative integer, x*y=? (1) 7^x=13^y (2)

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If x and y are none negative integer, x*y=? (1) 7^x=13^y (2) [#permalink]

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25 Jul 2008, 03:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

. If x and y are none negative integer, x*y=?
(1) 7^x=13^y
(2) 3^x=9^y
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25 Jul 2008, 04:23
arjtryarjtry wrote:
. If x and y are none negative integer, x*y=?
(1) 7^x=13^y
(2) 3^x=9^y

(2) is not sufficient:

3^x = 9^y
3^x = 3^(2y)
x = 2y

All (2) tells us is that x is twice as large as y.

(1) is sufficient:

7^x=13^y

If x > 0, then 7 is a divisor of the left side of the equation. Then 7 must be a divisor of the right side. But clearly it cannot be- the only prime that can divide the right side is 13. Here, of course, we're using unique factorization into primes. So x = y = 0.
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Re: powers of integer   [#permalink] 25 Jul 2008, 04:23
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