The total number of solutions of

2^x+3^x+4^x-5^x=0 is/are...........

hi, above eqn can be written as 2^x + 3^x + 4^x = 5^x functions on both sides of equality are increasing functions so, either they will not meet or they will meet at a single point for greater +ve values of x, 5^x much steeper & for x <0, L.H.S. > R.H.S. hence we can say ,there is only a single point for which L.H.S. = R.H.S. so, no. of soln. = 1