These questions are from several math contests, and I'm trying to do these but I can't figure it out.
1. If x and y > 0 , log(base y)x + log(base x)y = 10/3 ,and (x)(y)=144
,find x + y /2
2. How many real numbers x satisfy the equation (1/5) log(base 2)x = sin(5pi x) ?
I tried making y=144/x and plugging that into the equation, but I have no idea what to do for the second question
Any help from you guys is greatly appreciated :)