Question

the no. of solution of 2^x+3^x+4^x=5^x is

Answer 1

hlo...the no. of solutions is 4

Answer 2

Say, f(x) = 2^x + 3^x + 4^x - 5^x = 0

For, x <=2, f(x) is positive.

For, x >=3, f(x) is negative.

So, there has to be at least one value of x that is between 2 and 3.

The value of x correct to 50 decimal places is

2.3732943684104698305305955807659755150751455928776

As function f(x) is monotonic, there cannot be more than one value of x between 2 and 3. Had it not been monotonic, there could have been 3, 5 or any odd number of values between 2 and 3.