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**lllll** I'm having a great of difficulty showing $\displaystyle |\ln(x)| \leq \frac{1}{\sqrt{x}}$ on the interval $\displaystyle (0,1]$

I was thinking that $\displaystyle |\ln(x)|$ can be written as $\displaystyle -\ln(x)$ since the given values will simply be reflected, which would give me

$\displaystyle 0 \leq \underbrace{\frac{1}{\sqrt{x}}}_{\mbox{always}\ >0}+\ln(x)$

but I'm stuck with the natural logarithm.

another think that I was thinking about was to show that the function never cross on the given interval, but I don't know how

that would be so since the both tend to infinity as they approach 0.