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If 125^x = 25^y  and x, y are non-zero, find x : y . A. 1 : 25 B. 1 : 5 C. 2 : 3 D. 3...

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christiano-cr7 | (Level 1) Salutatorian

Posted October 1, 2013 at 3:05 AM via web

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If 125^x = 25^y  and x, y are non-zero, find x : y .

A. 1 : 25

B. 1 : 5

C. 2 : 3

D. 3 : 2

E. 5 : 1

1 Answer | Add Yours

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted October 1, 2013 at 3:11 AM (Answer #1)

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`125^x = 25^y`

We know that for indices;

`(a^p)^q = a^(pq)`

`125^x = (5^3)^x = 5^(3x)`

`25^y = (5^2)^y = 5^(2y)`

`5^(3x) = 5^(2y)`

Since 5 is common for both 3x = 2y

`3x = 2y`

`x/y = 2/3`

`x:y = 2:3`

So the answer is C.

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