Mock AIME I 2015 Problems/Problem 2
Problem
Suppose that and
are real numbers such that
and
. The value of
can be expressed in the form
where
and
are positive relatively prime integers. Find
.
Corrected Solution and Answer
Use the logarithmic identity to expand the assumptions to
and
Solve for the values of and
which are respectively
and
The sought ratio is
The answer then is
Solution by D. Adrian Tanner (Original solution and answer below)
Original Solution
By rearranging the values, it is possible to attain an
x= 3^ (65/17)
and
y= 3^ (33/17)
Therefore, a/b is equal to 25/61, so 25+41= 061