Let ( x ) and ( y ) be real numbers satisfying ( 2x = 125 ) and ( 3y = 25 ). The number ( log₅ 6 ) can be expressed in the form ( ax + by + xy ), where ( a ) and ( b ) are both integers. Determine ( a ) and ( b ).
a) ( a = 2, b = 3 )
b) ( a = 3, b = 2 )
c) ( a = 4, b = 1 )
d) ( a = 1, b = 4 )
