I have a few expressions and need to get a final simplified (reduced,solved) results. I am new and tried/searched different ways for my problem but couldn't find the reason. These are my expressions:
R0 = FractionalPart[Log[5, x + (3/ 4)]] == FractionalPart[Log[5, xP + (3/ 4)]]
R1 = Log[5, xP + (3 / 4)] - Log[3, yP + ( 5 / 2)] == Log[5, x + (3 / 4)] - Log[3, y + ( 5 / 2)]
F = ( (x == xP && y == yP) || ( Exists[{xPP, yPP}, xPP < yPP && xP == 5 xPP + 3 && yP == 3 yPP + 5]))
R = R0 && R1 && F
Reduce[R && xP >= yP , {x, y, xP, yP}, Reals]
when I run this it takes a long time and seems infinite loop or something and never finishes. I also tried this
Reduce[R , Element[{x, y, xP, yP}, Reals]]
and it returns the error: Reduce : This system cannot be solved with the methods available to Reduce We expect two functions for xP and yP based on x and y, for each. Please help me through this.
2- How can I make sure that each single expression is error free? Thanks a lot