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

`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.*

**Sources:**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes