SOLUTION: I'm supposed to find all solutions of x^1/logx=5. I'm pretty sure there are no real solutions but don't know how to show that this is true. Can anyone tell me how to work this?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I'm supposed to find all solutions of x^1/logx=5. I'm pretty sure there are no real solutions but don't know how to show that this is true. Can anyone tell me how to work this?      Log On


   

Question 241712: I'm supposed to find all solutions of x^1/logx=5.
I'm pretty sure there are no real solutions but don't know how to show that this is true. Can anyone tell me how to work this?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^1/logx=5.
log%28x%5E%28%281%2Flog%28x%29%29%29%29+=+log%285%29
%281%2Flogx%29%2Alog%28x%29+=+log%285%29
log(5) = 1
log%28x%5E%28%281%2Flog%28x%29%29%29%29+=+1 for any x>0