find the number of solution of the equation 3^x+4^x=5^x
For x<=1, value is positive.
For x>=3, value is negative.
So the value of x lies in between 1 and 3.
The only number satisfying the equation is 2. So number of solution is 1.
divide directly by 5^x and get 1=(3/5)^x+(4/5)^x1. From here it is clear that the RHS is strictly decreasing, and there is a unique solution