# 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

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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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