### Given the following equations:

**5**^{(a+b)} = 3125, and

**3125**^{(a-b)} = 5,

what is the value of b?

^{(a+b)}= 3125

^{(a-b)}= 5

**Answer:**

12 |

5 |

**Step by Step Explanation:**

- We know that 3125 = 5
^{5}. If we replace 3125 by 5 to the power 5, we get:

5^{5(a-b)}= 5

5^{(a+b)}= 5^{5} - From the above step we have:

5(a - b) = 1

or, 5a - 5b = 1 ------(1)

a + b = 5 ------(2)

or, 5a + 5b = 25 ------(3)**[On multiplying by 5.]** - Adding equation (1) and (3) we have:

10a = 26

Or, a =13 5 - Putting this value in equation (2) we get:

b = 5 - a

Or, b = 5 -13 5

Or, b =12 5