I think this one was missed out:

3^x+4^x = 5^x

 

Rewrite as (3/5)^x+(4/5)^x = 1

x=2 is a solution. To check if any other solutions

 

Let f(x) = (3/5)^x+(4/5)^x -1

 

This is a monotonically decreasing function. It is easy to see that there are no solutions (-inf,2) and also (2, inf)

Hence x=2 is the unique soln.