Problem:
The value of that satisfies can be written as , where and are relatively prime positive integers. Find .
Solution:
We can simplify the given expression by converting everything to .
Write the left hand side of the expression as and the right hand side as .
Using the power rule for logarithms, we can simplify further to
Equating the exponents of inside the logs, we get .
Solving, and the requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions