statement:`e^pi` is bigger than `pi^e` statement 2:`f(x)=x^(1/x)` is an increasing function whenn `xe[e,oo)`

statement1: e^pi is bigger than pi^e statement 2: f(x)=x^(1/x) is an increasing function whenn xe[e,oo)

Statement-1 e^(pi) gt pi^( e) Statement -2 The function x^(1//x)( x gt 0) is strictly decreasing in [e ,oo)

Statement-1 e^(pi) gt pi^( e) Statement -2 The function x^(1//x)( x gt 0) is strictly decreasing in [e ,oo)

Statement-1: e^(x)+e^(-x)>2+x^(2),x!=0 Statement-2: f(x)=e^(x)+e^(-x)-2-x^(2) is an increasing function.

Consider the following statements 1 f(x)=In x is an increasing funciton on (0,oo) 2 f(x) =e^(x)-x(In x) is an increasing function on (1,oo) Which of the above statement is / are correct ?

Prove that the function f(x)=(log)_(e)x is increasing on (0,oo)

Prove that the function f(x)=log_(e)x is increasing on (0,oo)

Prove that the function f(x)=(log)_e x is increasing on (0,\ oo) .

Statement 1: pi^(4) gt 4^(pi) because Statement 2 : The function y = x^(x) is decreasing forall x gt 1/e .