Prove that function `f(x) = log_e x` is strictly increasing in the interval `(0,oo)`

Prove that the function f(x) = 10^(x) is strictly increasing on R

The function f(x) = 7 + x - e^(x) is strictly increasing in the interval

Prove that the function f(x)=x^(2)+2 is strictly increasing in the interval (2,7) and strictly decreasing in the interval (-2, 0).

Show that the function f(x) = log (sin x) (i) is strictly increasing in the interval ]0,pi/2[ . (ii) is strictly decreasing in the interval ]pi/2,pi[ .

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

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

Prove that f (x) = e^(3x) is strictly increasing function on R.

Prove that f (x) = e^(3x) is strictly increasing function on R.

Show that the function f(x)= x^(2) is strictly increasing function in the interval ]0,infty[ .