Problem:
Positive real numbers and satisfy the equations
The value of is , where and are relatively prime positive integers. Find .
Solution:
Let . Then the system of equations given in the problem becomes:
Solving this system yields and .
Therefore,
4n = b^x = \left(\frac{5}{4}\right)^4 = \frac{625}
So, the final answer is:
625 + 256 = \boxed
The problems on this page are the property of the MAA's American Mathematics Competitions