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
and
Therefore, a/b is equal to 25/61, so 25+41= 061
Ignore the original solution as it is incorrect - blunderbro Solution at the top checked by blunderbro Note: It is correct, original one was the first one posted but was incorrect.