# How to prove that log(x)1x>1?

It’s very basic but I’m having trouble to find a way to prove this inequality

$$log(x)

when $$x>1x>1$$

($$log(x)\log(x)$$ is the natural logarithm)

I can think about the two graphs but I can't find another way to prove it, and, besides that, I don't understand why should it not hold if $$x<1x<1$$

Can anyone help me?

and $f$ is strictly decreasing, then