$f(n)=n^{\frac{1}{\sqrt{\log n}}}= e^{\log n^{\frac{1}{\sqrt{\log n}}}}=e^{\sqrt{\log n}}$
$g(n)=\sqrt{\log n}=e^{\log \sqrt{\log n}}$
$h(n)=n^{\frac{1}{100}}=e^{\log n^{\frac{1}{100}} }=e^{k \times \log n}$
$g(n)\, < \,f(n) \, <h(n)$
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